influence analysis of ranking data this paper develops diagnostic measures to identify those observations in thurstonian models for ranking data which unduly influence parameter estimates that are obtained by the partition maximum likelihood approach of chan and bentler 1998 diagnostic measures are constructed by employing the local influence approach that uses geometric techniques to assess the effect of small perturbations on a postulated statistical model very little additional effort is required to compute the proposed diagnostic measures because all of the necessary building blocks are readily available after a usual fit of the model

adding handles to the helicoid there exist two new embedded minimal surfaces asymptotic to the helicoid one is periodic with quotient by orientation preserving translations of genus one the other is nonperiodic of genus one

estimation for partially nonstationary multivariate autoregressive models abstract for an m variate partially nonstationary vector autoregressive process y t we consider the autoregressive model l y t e t where l i 1 l p l p and det z 0 has d m roots equal to unity and all other roots are outside the unit circle it is also assumed that rank 1 r r m d so that each component of the first differences w t y t y t 1 is stationary the relation of the model to error correction models and co integration engle and granger 1987 is discussed the process y t has the error correction representation l 1 l y t p 2 i r r q 2 1 y t 1 e t where q i m 1 p j diag i d r is in jordan canonical form and q q 1 q 2 it follows that the transformation z t qy t zt 1t z2 2t t is such that the d 1 process z 1t is nonstationary with z 1t z 1t 1 stationary while z 2t is stationary asymptotic distribution theory for least squares parameter estimators of the model is first considered a gaussia

leverage local influence and curvature in nonlinear regression summary the connections between measures of leverage statistical curvature and the local influence of a mean shift perturbation are explored in nonlinear regression models the circumstances under which the jacobian leverage reduces to a commonly used linear approximation are found to be connected to the effective residual curvature of the nonlinear model the local influence of a mean shift perturbation in the model function is seen to be closely related to the jacobian leverage

on properly embedded minimal surfaces with three ends we classify all complete embedded minimal surfaces in r with three ends of genus g and at least 2g 2 symmetries the surfaces in this class are the costa hoffman meeks surfaces which have 4g 4 symmetries in the case of a flat middle end the proof consists of using the symmetry assumptions to deduce the possible weierstras data and then to study the period problems in all cases to handle the 1 dimensional period problems we develop a new general method to prove convexity results for period quotients the 2 dimensional period problems are reduced to the 1 dimensional case by an extremal length argument 1991 mathematics subject classification primary 53a10 secondary 53c42

classification of rotational special weingarten surfaces of minimal type in mathbb s 2 times mathbb r and mathbb h 2 times mathbb r in this paper we classify the complete rotational special weingarten surfaces in mathbb s 2 times mathbb r and mathbb h 2 times mathbb r i e rotational surfaces in mathbb s 2 times mathbb r and mathbb h 2 times mathbb r whose mean curvature h and extrinsic curvature ke satisfy h f h2 ke for some function f in mathcal c 1 0 infty such that f 0 0 and 4x f x 2 1 for any x 0 furthermore we show the existence of non complete examples of such surfaces

serrin s overdetermined problem and constant mean curvature surfaces for all n 9 we find smooth entire epigraphs in rn namely smooth domains of the form x rn xn f x1 xn 1 which are not half spaces and in which a problem of the form u f u 0 in has a positive bounded solution with 0 dirichlet boundary data and constant neumann boundary data on this answers negatively for large dimensions a question by berestycki caffarelli and nirenberg in 1971 serrin proved that a bounded domain where such an overdetermined problem is solvable must be a ball in analogy to a famous result by alexandrov that states that an embedded compact surface with constant mean curvature cmc in euclidean space must be a sphere in lower dimensions we succeed in providing examples for domains whose boundary is close to large dilations of a given cmc surface where serrin s overdetermined problem is solvable

on the topology and index of minimal surfaces we show that for an immersed two sided minimal surface in r 3 there is a lower bound on the index depending on the genus and number of ends using this we show the nonexistence of an embedded minimal surface in r 3 of index 2 as conjectured by choe cho90 moreover we show that the index of an immersed two sided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface

embedded minimal surfaces of finite topology in this paper we prove that any complete embedded minimal surface m in r 3 with finite topology and compact boundary possibly empty is conformally a compact riemann surface m with boundary punctured in a finite number of interior points and that m can be represented in terms of meromorphic data on its conformal completion m in particular we demonstrate that m is a minimal surface of finite type and describe how this property permits a classification of the asymptotic behavior ofm

embedded minimal surfaces with an infinite number of ends we prove the existence of an infinite family of periodic properly embedded minimal surfaces with an infinite number of annular ends 25 refs 29 figs

a three stage estimation procedure for structural equation models with polytomous variables this paper is concerned with the analysis of structural equation models with polytomous variables a computationally efficient three stage estimator of the thresholds and the covariance structure parameters based on partition maximum likelihood and generalized least squares estimation is proposed an example is presented to illustrate the method

local influence in principal components analysis summary based on the definition of generalised influence function and generalised cook statistic local influence of small perturbations on the eigenvalues and eigenvectors of a covariance matrix are studied for population and sample versions the results based on the correlation matrix are also derived and some related topics are discussed finally an example is used for illustration bations although this method has been applied to many models beckman nachtsheim cook 1987 lawrance 1988 thomas cook 1990 assessing the local influence for multivariate data is still an unexplored area in this paper a method based on a generalised influence function and generalised cook statistic is introduced to assess the local influence of small perturbations on a statistic of interest and we prove that this method is equivalent to cook s work based on normal curvature in the likelihood framework since local influence on some statistics in multivariate analysis is not easy to study using the likelihood displacement of cook 1986 this method is expected to have wider applications in this paper we employ the generalised cook statistic to assess local influence in principal components analysis in 2 we introduce the definition of the generalised influ ence function and generalised cook statistic in 3 the perturbation theory of eigenvalues and eigenvectors of a real symmetric matrix is studied in 4 the local influence of small perturbations of observations on eigenvalues and the eigenvectors of sample covariance

local influence analysis of nonlinear structural equation models by regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete data log likelihood function in the em algorithm we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model the basic building blocks of local influence analysis are computed via observations of the latent variables generated by the metropolis hastings algorithm while the diagnostic measures are obtained via the conformal normal curvature seven perturbation schemes including some perturbation schemes on latent vectors are investigated the proposed procedure is illustrated by a simulation study and a real example

a costa hoffman meeks type surface in mathbb h 2 times mathbb r we show the existence in the space 2 x of a family of embedded minimal surfaces of genus 1 k and finite total extrinsic curvature with two catenoidal type ends and one middle planar end the proof is based on a gluing procedure

approximate power functions for some robust tests of regression coefficients approximate power functions for some robust tests of regression coefficients thomas j rothenberg department o f economics u n i v e r s i t y o f c a l i f o r n i a berkeley research papers i n economics no 84 1 summary edgeworth expansions are developed f o r the d i s t r i b u t i o n functions o f some t e s t s t a t i s t i c s i n the normal l i n e a r regression model where the e r r o r covariance matrix i s unknown tests based on generalized l e a s t squares estimates and also on ordinary l e a s t squares estimates are considered in both cases adjustments t o the asymptotic c r i t i c a l the approxi values are found and approximate l o c a l power c a l c u l a t e d and a u t o c o r r e l a t i o n mations are applied to a number o f examples i n c l u d i n g h e t e r o s c e d a s t i c i t y

on the growth of supersolutions of nonlinear pde s on exterior domains abstract we obtain a comparison principle on annuli with catenoid like functions for supersolutions of non linear elliptic pdes over exterior domains in a non positively curved manifold with a pole this result is applied to get an upper estimate on the growth of such supersolutions and in particular of exterior graphs of non negative mean curvature

the calabi yau conjectures for embedded surfaces in this talk i will discuss the proof of the calabi yau conjectures for embedded surfaces this is joint work with bill minicozzi cm9 the calabi yau conjectures about surfaces date back to the 1960s much work has been done on them over the past four decades in particular examples of jorge xavier from 1980 and nadirashvili from 1996 showed that the immersed versions were false we will show here that for embedded surfaces i e injective immersions they are in fact true their original form was given in 1965 in ca where e calabi made the following two conjectures about minimal surfaces see also s s chern page 212 of ch conjecture 1 prove that a complete minimal hypersurface in r must be unbounded calabi continued it is known that there are no compact minimal submanifolds of r or of any simply connected complete riemannian manifold with sectional curvature 0 a more ambitious conjecture is conjecture 2 a complete minimal hypersurface in r has an unbounded projection in every n 2 dimensional flat subspace

diagnostics for mixed model analysis of variance we describe a new method for assessment of model inadequacy in maximum likelihood mixed model analysis of variance in particular we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population computer implementation of the procedure is described and an example is presented involving the analysis of filter cartridges used with commercial respirators

the spaces of index one minimal surfaces and stable constant mean curvature surfaces embedded in flat three manifolds it is proved that the spaces of index one minimal surfaces and stable constant mean curvature surfaces with genus greater than one in non fixed flat three manifolds are compact in a strong sense given a sequence of any of the above surfaces we can extract a convergent subsequence of both the surfaces and the ambient manifolds in the ck topology these limits preserve the topological type of the surfaces and the affine diffeomorphism class of the ambient manifolds some applications to the isoperimetric problem are given

on local influence analysis of full information item factor models the full information item factor fiif model is very useful for analyzing relations of dichotomous variables in this article we present a feasible procedure to assess local influence of minor perturbations for identifying influence aspects of the fiif model the development is based on a q displacement function which is closely related with the monte carlo em algorithm in the ml estimation in the e step of this algorithm the conditional expectations are approximated by sample means of observations simulated by the gibbs sampler from the appropriate conditional distributions it turns out that these observations can be utilized for computing the building blocks of the proposed diagnostic measures the diagnoses are based on the conformal normal curvature that can be computed easily a number of interesting perturbation schemes are considered the methodology is illustrated with two real examples

the space of embedded minimal surfaces of fixed genus in a 3 manifold v fixed genus this paper is the fifth and final in a series on embedded minimal surfaces following our earlier papers on disks we prove here two main structure theorems for itnonsimply connected embedded minimal surfaces of any given fixed genus the first of these asserts that any such surface without small necks can be obtained by gluing together two oppositely oriented double spiral staircases the second gives a pair of pants decomposition of any such surface when there are small necks cutting the surface along a collection of short curves after the cutting we are left with graphical pieces that are defined over a disk with either one or two sub disks removed a topological disk with two sub disks removed is called a pair of pants both of these structures occur as different extremes in the two parameter family of minimal surfaces known as the riemann examples

diagnostics in categorical data analysis diagnostics as measures of model deviations and of the influence of particular data sets are used extensively in modern regression analysis for contingency tables and more generally for the parametric multinomial distribution it is not the influence of individual observations which is of interest but rather the contribution to a lack of model fit or to the values of the parameter estimates from a single cell in the table which must be evaluated hence diagnostics for contingency tables take somewhat different forms

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

constant mean curvature graphs on exterior domains of the hyperbolic plane we prove an existence result for non rotational constant mean curvature ends in mathbb h 2 times mathbb r where mathbb h 2 is the hyperbolic real plane the value of the curvature is h in big 0 frac 1 2 big we use schauder theory and a continuity method for solutions of the prescribed mean curvature equation on exterior domains of mathbb h 2 we also prove a fine property of the asymptotic behavior of the rotational ends introduced by sa earp and toubiana

sensitivity analysis of structural equation models the main purpose of this paper is to investigate the sensitivity analysis of structural equation model when minor perturbation is introduced some influence measure that based on the general case weight perturbation is derived for the generalized least squares estimation an influence measure that related to the cook s distance is also developed for the special case deletion perturbation scheme using the proposed methodology the influential observation in a data set can be detected moreover the general theory can be applied to detect the influential parameters in a model finally some illustrative artificial and real examples are presented

complete embedded minimal surfaces of finite total curvature we will survey what is known about minimal surfaces s r 3 which are complete embedded and have finite total curvature int s k da infty the only classically known examples of such surfaces were the plane and the catenoid the discovery by costa 14 15 early in the last decade of a new example that proved to be embedded sparked a great deal of research in this area many new examples have been found even families of them as will be described below the central question has been transformed from whether or not there are any examples except surfaces of rotation to one of understanding the structure of the space of examples

influence analysis of structural equation models with polytomous variables the estimation of model parameters in structural equation models with polytomous variables can be handled by several computationally efficient procedures however sensitivity or influence analysis of the model is not well studied we demonstrate that the existing influence analysis methods for contingency tables or for normal theory structural equation models cannot be applied directly to structural equation models with polytomous variables and we develop appropriate procedures based on the local influence approach of cook 1986 the proposed procedures are computationally efficient the necessary bits of the proposed diagnostic measures are readily available following an usual fit of the model we consider the influence of an individual cell frequency with respect to three cases when all parameters in an unstructured model are of interest when the unstructured polychoric correlations are of interest and when the structural parameters are of interest we also consider the sensitivity of the parameters estimates two examples based on real data are presented for illustration

complete nonorientable minimal surfaces with the highest symmetry group in this paper we present a family of complete nonorientable highly symmetrical minimal surfaces with arbitrary topology and one end for each topology we construct the most symmetrical example with one end furthermore if the euler characteristic of the closed associated surface is even our examples minimize the energy or the degree of the gauss map among the surfaces with their symmetry topology and one end finally we characterize these surfaces in terms of their topology symmetry total curvature and number of ends

uniqueness of self similar shrinkers with asymptotically conical ends in this paper we show the uniqueness of smooth embedded selfshrinkers asymptotic to generalized cylinders of infinite order also we construct non rotationally symmetric self shrinking ends asymptotic to generalized cylinders with rate as fast as any given polynomial

a general structural equation model with dichotomous ordered categorical and continuous latent variable indicators a structural equation model is proposed with a generalized measurement part allowing for dichotomous and ordered categorical variables indicators in addition to continuous ones a computationally feasible three stage estimator is proposed for any combination of observed variable types this approach provides large sample chi square tests of fit and standard errors of estimates for situations not previously covered two multiple indicator modeling examples are given one is a simultaneous analysis of two groups with a structural equation model underlying skewed likert variables the second is a longitudinal model with a structural model for multivariate probit regressions

a small sample correction for tests of hypotheses on the cointegrating vectors abstract the main purpose of the analysis of the cointegrated var model is conducting inference on the cointegrating relations asymptotic inference is 2 but the asymptotic results are not accurate enough for small samples therefore we derive here a correction factor depending on sample size and parameters for the likelihood ratio test of some linear hypotheses on the cointegrating space in a vector autoregressive model we have to assume that the adjustment coefficients are known the main idea is to condition on the common trends when calculating the correction factor some simulation experiments illustrate the findings

a rigidity theorem for properly embedded minimal surfaces in bf r sp 3 we consider the question of when an intrinsic isometry of a properly embedded minimal surface is induced by an ambient isometry we prove it always extends when the surface has at least two ends there are several interesting theorems and conjectures on the rigidity of complete surfaces in r 3 which satisfy some natural geometric constraint perhaps the best known theorem of this type is the cohn vossen theorem which shows that a compact riemannian surface of positive curvature has a unique immersion into r a similar result is conjectured for complete surfaces of nonpositive or nonnegative curvature with the additional hypothesis that the surface has finite area it is also conjectured that tight surfaces are rigid in this paper we prove a rigidity theorem for properly embedded minimal surfaces in r 3 which have more than one end this theorem states that the inclusion map of the surface into r3 represents the unique isometric minimal immersion of such a surface up to a rigid motion of r 3 in particular it follows from our theorem that every intrinsic isometry of this type of surface extends to an isometry of r 3 in 1 we derive a geometric condition on an immersed minimal surface which guarantees that the surface is minimally rigid we prove that if the surface intersects a plane transversally along an immersed closed curve then any other isometric minimal immersion of the surface into r differs from the original immersion by an ambient isometry in 2 we obtain some asymptotic properties of solutions of the minimal surface equation over annular planar domains in 3 we prove that if a properly embedded minimal surface m in r3 has more than one end then m is transverse

minimal surfaces from circle patterns geometry from combinatorics the theory of polyhedral surfaces and more generally the field of discrete differential geometry are presently emerging on the border of differential and discrete geometry whereas classical differential geometry investigates smooth geometric shapes such as surfaces and discrete geometry studies geometric shapes with a finite number of elements polyhedra the theory of polyhedral surfaces aims at a development of discrete equivalents of the geometric notions and methods of surface theory the latter appears then as a limit of the refinement of the discretization current progress in this field is to a large extent stimulated by its relevance for computer graphics and visualization one of the central problems of discrete differential geometry is to find proper discrete analogues of special classes of surfaces such as minimal con stant mean curvature isothermic surfaces etc usually one can suggest vari ous discretizations with the same continuous limit which have quite different geometric properties the goal of discrete differential geometry is to find a dis cretization which inherits as many essential properties of the smooth geometry as possible our discretizations are based on quadrilateral meshes i e we discretize parametrized surfaces for the discretization of a special class of surfaces it is natural to choose an adapted parametrization in this paper we investigate conformai discretizations of surfaces i e discretizations in terms of circles and spheres and introduce a new discrete model for minimal surfaces see figures 1 and 2 in comparison with direct methods see in particular 23 leading

the strong halfspace theorem for minimal surfaces d hoffman and w h meeks iii department of mathematics university of massachusetts amherst ma 01003 usa in 6 jorge and xavier constructed examples of complete nonplanar minimal surfaces contained between two parallel planes in 3 recently rosenberg and toubiana have found complete minimally immersed annuli that are proper in an open slab 1 12 on the basis of these and other results the question has arisen as to whether or not there could exist a properly immersed minimal surface in 3 that was contained between two parallel planes the answer is negative an immediate consequence of the following theorem

equivariant minimax and minimal surfaces in geometric three manifolds minimal surfaces in riemannian three dimensional manifolds have played a major role in recent studies of the geometry and topology of 3 manifolds in particular stable and least area minimal surfaces have been used extensively sy msy hs on the other hand explicit examples of unstable minimal surfaces have rarely been given for the 3 sphere s with the standard metric of constant sectional curvature there is the classical paper of lawson lh showing that closed orientable surfaces of every genus occur as unstable minimal surfaces embedded in 5 3 more recently karcher pinkall and sterling kps have constructed several new examples in s we have discovered new infinite families of minimal surfaces in s more generally we announce a number of new finite and infinite families of embedded minimal surfaces in geometric 3 manifolds using the minimax procedure described below geometric structures on 3 manifolds were introduced by thurston tw see also the excellent survey by scott sp1 there are eight geometries r s s x r nil h 2 x r s l r solv and h a geometric structure on a 3 manifold s is a representation of e as a quotient of one of the above eight spaces divided out by a covering transformation group acting isometrically equivalently e is locally isometric to one of these spaces with its natural homogeneous space structure the first six of these geometries give seifert fiber spaces and we are mainly interested in such examples the so 2 isometry actions associated with most seifert fiber spaces yield infinite classes of embedded minimal surfaces note that interesting examples can also be obtained in the other two geometries e g in hyperbolic geometry h 3 pr3 2 the minimax procedure has proved to be a versatile and powerful means of constructing unstable minimal surfaces in 3 manifolds for basic details of this technique see pj ss p r l and pr2 suppose that g is a finite group of isometries acting on a closed oriented riemannian 3 manifold e assume that a is a heegaard surface in e i e the closures of the components of e a are handlebodies k and k assume furthermore that a is g equivariant i e ga a for all g e g we consider one parameter smooth families at t 0 1 sweeping out e and having the following properties ao and ai are graphs at is isotopic to a for all 0 t 1 at is g equivariant for all t the handlebody kt is chosen so that the orientation on at is induced from that on

the classical theory of minimal surfaces we present here a survey of recent spectacular successes in classical minimal surface theory we highlight this article with the theorem that the plane the helicoid the catenoid and the one parameter family frtgt2 0 1 of riemann minimal examples are the only complete properly embedded minimal planar domains in r 3 the proof of this result depends primarily on work of colding

minimal hypersurfaces with bounded index we prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index and volume if the ambient dimension is greater than three in a riemannian manifold m n g 3 le n le 7 can degenerate loosely speaking our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embedded stable minimal hypersurfaces up to controlled errors several compactness finiteness theorems follow from our local picture

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

entire solutions of the allen cahn equation and complete embedded minimal surfaces of finite total curvature in r 3 we consider minimal surfaces m which are complete embedded and have finite total curvature in mathbb r 3 and bounded entire solutions with finite morse index of the allen cahn equation delta u f u 0 in mathbb r 3 here f w with w bi stable and balanced for instance w u frac 1 4 1 u 2 2 we assume that m has m ge 2 ends and additionally that m is non degenerate in the sense that its bounded jacobi fields are all originated from rigid motions this is known for instance for a catenoid and for the costa hoffman meeks surface of any genus we prove that for any small alpha gt 0 the allen cahn equation has a family of bounded solutions depending on m 1 parameters distinct from rigid motions whose level sets are embedded surfaces lying close to the blown up surface m alpha alpha 1 m with ends possibly diverging logarithmically from m alpha we prove that these solutions are l infty non degenerate up to rigid motions and find that their morse index coincides with the index of the minimal surface our construction suggests parallels of de giorgi conjecture for general bounded solutions of finite morse index

maximum likelihood estimation of multivariate polyserial and polychoric correlation coefficients the method of finding the maximum likelihood estimates of the parameters in a multivariate normal model with some of the component variables observable only in polytomous form is developed the main stratagem used is a reparameterization which converts the corresponding log likelihood function to an easily handled one the maximum likelihood estimates are found by a fletcher powell algorithm and their standard error estimates are obtained from the information matrix when the dimension of the random vector observable only in polytomous form is large obtaining the maximum likelihood estimates is computationally rather labor expensive therefore a more efficient method the partition maximum likelihood method is proposed these estimation methods are demonstrated by real and simulated data and are compared by means of a simulation study

higher genus riemann minimal surfaces riemann surfaces constitute a one parameter family of embedded minimal surfaces which are periodic and have infinitely many horizontal planar ends the surfaces in this family are foliated by circles or straight lines in this paper we prove the existence of a one parameter family of embeded minimal surfaces which have infinitely many horizontal planar ends and have genus k for k 1 37 riemann surfaces as their flux is nearly vertical can be understood as a sequence of parallel planes connected by slightly bent catenoidal neks the surfaces we construct are obtained by replacing one of these catenoidal necks by a member of the family of minimal surfaces discovered by c costa d hoffman and w meek

triply periodic constant mean curvature surfaces abstract given a closed flat 3 torus n for each h 0 and each non negative integer g we obtain area estimates for closed surfaces with genus g and constant mean curvature h embedded in n this result contrasts with the theorem of traizet 31 who proved that every flat 3 torus admits for every positive integer g with g 2 connected closed embedded minimal surfaces of genus g with arbitrarily large area

regression transformation diagnostics using local influence abstract following box and cox 1964 the use of transformations in regression analysis is now common recently there has been emphasis on diagnostic methods for transformation much of which has involved deletion of data cases summaries were given by cook and weisberg 1982 and atkinson 1985 this article obtains diagnostics for the estimated regression parameter of the box cox transformation of the response variable in the linear model instead of deleting cases the more general notions of perturbing assumptions of the model or components of the data are employed as in the local influence approach of cook 1986 the diagnostics then arise from local changes to the transformation parameter estimate caused by small perturbations the case direction in which small perturbations have the greatest effect is the main diagnostic quantity an appeal of the approach is that it allows simultaneous perturbations affecting all data cases not just one at a time deletions it can thus point to groups of in

finite topology self translating surfaces for the mean curvature flow in r3 abstract finite topology self translating surfaces for the mean curvature flow constitute a key element in the analysis of type ii singularities from a compact surface because they arise as limits after suitable blow up scalings around the singularity we prove the existence of such a surface m r 3 that is orientable embedded complete and with three ends asymptotically paraboloidal the fact that m is self translating means that the moving surface s t m t e z evolves by mean curvature flow or equivalently that m satisfies the equation h m e z where h m denotes mean curvature is a choice of unit normal to m and e z is a unit vector along the z axis this surface m is in correspondence with the classical three end costa hoffman meeks minimal surface with large genus which has two asymptotically catenoidal ends and one planar end and a long array of small tunnels in the intersection region resembling a periodic scherk surface this example is the first non trivial one of its kind and it suggests a strong connection between this problem and the theory of embedded complete minimal surfaces with finite total curvature

a schoen theorem for minimal surfaces in h 2 r abstract in this paper we prove that a complete minimal surface immersed in h 2 r with finite total curvature and two ends each one asymptotic to a vertical geodesic plane must be a horizontal catenoid moreover we give a geometric description of minimal ends of finite total curvature in h 2 r we also prove that a minimal complete end e with finite total curvature is properly immersed and that the gaussian curvature of e is locally bounded in terms of the geodesic distance to its boundary

the doubly periodic costa surfaces we derive global weierstrass representations for complete minimal surfaces obtained by substituting the planar end of the costa surface by symmetry curves

constant mean curvature surfaces in m 2 times mathbf r the subject of this paper is properly embedded h surfaces in riemannian three manifolds of the form m 2 x r where m 2 is a complete riemannian surface when m 2 r 2 we are in the classical domain of h surfaces in r 3 in general we will make some assumptions about m 2 in order to prove stronger results or to show the effects of curvature bounds in m 2 on the behavior of h surfaces in m 2 x r

assessing influence on predictions from generalized linear models influence diagnostics for predictions from a normal linear model examine the effect of deleting a single case on either the point prediction or the predictive density function instead of deleting cases we apply the local influence method of cook 1986 to assess the effect of small perturbations of continuous data on a specified point prediction from a generalized linear model based on local perturbations of the vector of responses case weights explanatory variables or the components of one case the diagnostics can detect different kinds of influence some of the diagnostics are illustrated with an example and compared to standard diagnostic methods

the classification of complete minimal surfaces with total curvature greater than 12 we classify complete orientable minimal surfaces with finite total curvature 87r introduction the classification of complete minimal surfaces with finite total curvature in r3 has been an important problem in the classical differential geometry some basic properties of these surfaces were studied by r osserman see 8 9 who showed the first nontrivial result about this subject concretely he characterized the catenoid and enneper surface as the unique complete orientable minimal surfaces of total curvature 47 however until recent years no more relevant results have been obtained w h meeks 6 gave the classification of nonorientable complete minimal surfaces with total curvature greater than 87 this paper is concerned with the total classification of orientable complete minimal surfaces with total curvature 87 chen and gackstatter 1 discovered the first example of a complete minimal surface properly of genus 1 see theorem 1 the picture of chen gackstatter surface is obtained by joining a handle on enneper s surface this genus one minimal surface has total curvature 87 and no other examples of such surfaces were found so it is expected that no other genus one orientable minimal surface of total curvature 87 does exist in this paper we give a proof of this fact more precisely we prove that chen gackstatter surface is the only genus one orientable complete minimal surface with finite total curvature 87 of course it is not difficult to find genus zero minimal surfaces with total curvature 8i a geometrically interesting example described by jorge and meeks 5 is the trinoid this surface has three embedded catenoid ends moreover its normal vectors at these ends are placed symmetrically in an equator of s2 received by the editors april 27 1990 and in revised form july 20 1990 1980 mathematics subject classification 1985 revision primary 53a10 research partially supported by dgicyt grant ps87 01 15 c03 02

on the estimation of polychoric correlations and their asymptotic covariance matrix a general theory for parametric inference in contingency tables is outlined estimation of polychoric correlations is seen as a special case of this theory the asymptotic covariance matrix of the estimated polychoric correlations is derived for the case when the thresholds are estimated from the univariate marginals and the polychoric correlations are estimated from the bivariate marginals for given thresholds computational aspects are also discussed

the embedded singly periodic scherk costa surfaces we give a positive answer to m traizet s open question about the existence of complete embedded minimal surfaces with scherk ends without planar geodesics in the singly periodic case these examples get close to an extension of traizet s result concerning asymmetric complete minimal submanifolds of open image in new window with finite total curvature

the space of complete minimal surfaces with finite total curvature as lagrangian submanifold the space m of nondegenerate properly embedded minimal surfaces in r3 with finite total curvature and fixed topology is an analytic lagrangian submanifold of cn where n is the number of ends of the surface in this paper we give two expressions one integral and the other pointwise for the second fundamental form of this submanifold we also consider the compact boundary case and we show that the space of stable nonflat minimal annuli that bound a fixed convex curve in a horizontal plane having a horizontal end of finite total curvature is a locally convex curve in the plane c mathematics subject classification 53a10 53c42

finite type annular ends for harmonic functions in this paper we describe the notion of an annular end of a riemann surface being of finite type with respect to some harmonic function and prove some theoretical results relating the conformal structure of such an annular end to the level sets of the harmonic function as an application of these results we obtain important information on the conformal type of any properly immersed minimal surface m in mathbb r 3 with compact boundary and which intersects some plane transversely in a finite number of arcs in particular such an m is a parabolic riemann surface this information is applied by meeks iii and perez embedded minimal surfaces of finite topology 2015 to classify the asymptotic behavior of annular ends of a complete embedded minimal annulus with compact boundary in terms of the flux vector along its boundary in the present paper we apply this information to understand and characterize properly immersed minimal surfaces in mathbb r 3 of finite total curvature in terms of their intersections with two nonparallel planes