properly embedded minimal planar domains in 1997 collin proved that any properly embedded minimal surface in r 3 with nite topology and more than one end has

opening nodes on horosphere packings we use bryant representation to construct constant mean curvature 1 surfaces in hyperbolic space by desingularisation of a horosphere packing

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

l 2 estimates for the boundary laplacian operator on hypersurfaces on donne une condition necessaire pour l estimation maximale pour le laplacien limite sur une hypersurface lisse m dans c n 1 non necessairement pseudoconvexe pour certaines classes d hypersurfaces on montre que la condition est aussi suffisante

microlocalisation et estimations pour mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagafyoaiyrbae badawgaawcbagaamoyaaqabaaaaa 387e bar partial _b dans quelques hypersurfaces pseudoconvexes nous etudions des estimations precises pour bar partial b sur des hypersurfaces dont la matrice de levi dans une base a une certaine forme en particulier nous donnons par la methode de microlocalisation une demonstration tres simple des estimations dites maximales lorsque les valeurs propres sont comparables nous obtenons en fait une precision supplementaire inegalite 3 17 qui permet de considerer des cas plus generaux finalement de telles estimations on deduit des estimations sous elliptiques optimales pour bar partial b

uniqueness of the riemann minimal examples we prove that a properly embedded minimal surface in r 3 of genus zero with infinite symmetry group is a plane a catenoid a helicoid or a riemann minimal example we introduce the language of hurwitz schemes to understand the underlying moduli space of surfaces in our setting

on maximal sobolev and holder estimates for the tangential cauchy riemann operator and boundary laplacian let m be the boundary of a smoothly bounded pseudoconvex domain in c n n 3 or more generally any compact pseudoconvex cr manifold of dimension 2 n 1 for which the range of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i is closed in l 2 in this article we study the l p sobolev and holder regularity properties of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i and b near a point of finite type under a comparable eigenvalues condition on the levi form we show that if all possible sums of q 0 eigenvalues of the levi matrix are comparable to its trace near a point of finite commutator type condition d q 0 then the inverse k q of b on 0 q forms for q 0 q n 1 q 0 satisfies sharp kernel estimates in terms of the quasi distance associated to the hormander sum of squares operator in particular we obtain the maximal l p estimates for b which were conjectured in the 1980s we also prove sharp estimates for certain parts of the kernels of k q 0 1 and k n q 0 and give some applications concerning domains with at most one degenerate eigenvalue finally we establish the composition and mapping properties of a class of singular integral nonisotropic smoothing operators that arises naturally in complex analysis these results yield optimal regularity of k q and related operators in the sobolev and lipschitz norms both isotropic and nonisotropic

an embedded minimal surface with no symmetries we construct embedded minimal surfaces of finite total curvature in euclidean space by gluing catenoids and planes we use weierstrass representation and we solve the period problem using the implicit function theorem as a corollary we obtain the existence of minimal surfaces with no symmetries

two end solutions to the allen cahn equation in r3 abstract in this paper we study axially symmetric solutions of allen cahn equation in the three dimensional euclidean space using a sophisticated continuation method we show the existence of a complete family of axially symmetric solutions with a range of logarithmic growth rates which may be regarded as the analogue of the family of catenoids and hence called two end solutions nonexistence of two end solution with a small growth rate is also shown which differs from the theory of minimal surfaces

complete embedded minimal surfaces of finite total curvature with planar ends of smallest possible order using a method by traizet j differ geom 60 103 153 2002 which reduces the construction of minimal surfaces via the weierstras theorem and the implicit function theorem to solving algebraic equations in several complex variables we will show the existence of complete embedded minimal surfaces of finite total curvature with planar ends of least possible order

a parametrix for the neumann problem on pseudoconvex domains of finite type abstract we construct a parametrix for the neumann problem on any pseudoconvex domain of finite type which reduces completely the study of isotropic lp sobolev and holder estimates to those for b and b we also establish the maximal nonisotropic estimates in the case of d q domains and provide a precise comparison of the bergman and szego projections and of the canonical solutions to with respect to these two operators the argument is substantially simpler than the known ones for the cases of strongly pseudoconvex domains and pseudoconvex domains of finite type in c 2

stability analysis of piecewise affine systems using controlled invariant sets abstract this paper presents new stability conditions for closed loop piecewise affine pwa systems the result is based on controlled invariant sets for pwa systems which are defined by extending the notion of semi ellipsoidal invariant sets for constrained linear systems reported in previous research the paper shows that by proper use of the control input concatenations of semi ellipsoidal sets can be made invariant for the trajectories of pwa systems furthermore based on these controlled invariant sets the paper presents a result for stability of a closed loop pwa system which is less conservative than existing approaches in the literature in this result it is shown that a pwa system is stable inside the intersection of any level set for a local lyapunov function and the design set where the function is defined provided the flow points inwards at the boundaries of the intersection this result is less conservative than previous approaches and it enables the designer to have an estimation of a much larger region of exponential stability then it would be possible using previous results a numerical example is presented in which it is made clear by comparison with previous approaches that the estimated region of stability can be made significantly larger using the new stability conditions developed in this paper

technical communique stability analysis for a class of digital filters with single saturation nonlinearity in this paper a new stability criterion for a class of digital filters with single saturation nonlinearity is presented in the form of a linear matrix inequality numerical examples are given to show the effectiveness of the obtained results

stability analysis of piecewise discrete time linear systems presents a stability analysis method for piecewise discrete time linear systems based on a piecewise smooth lyapunov function it is shown that the stability of the system can be established if a piecewise lyapunov function can be constructed and moreover the function can be obtained by solving a set of linear matrix inequalities lmis that is numerically feasible with commercially available software

solutions without any symmetry for semilinear elliptic problems abstract we prove the existence of infinitely many solitary waves for the nonlinear klein gordon or schrodinger equation u u u 3 0 in r 2 which have finite energy and whose maximal group of symmetry reduces to the identity

maximal hypoellipticity for the neumann problem abstract we establish maximal hypoellipticity for the neumann problem on smooth bounded pseudoconvex domains in c n under the weakest possible condition on the levi form in particular maximal hypoellipticity holds on the level of n 1 forms for pseudoconvex domains of finite commutator type

stability of linear discrete dynamics employing state saturation arithmetic this note is concerned with the stability of discrete time dynamical systems employing saturation arithmetic in the state space a matrix measure is introduced so that it can administer the proximity evaluation of a matrix to the set of diagonal matrices and the measure is utilized for making an additional condition to the lyapunov stein matrix inequality the solvability of the modified matrix inequality ensures not only the stability but also the absence of overflow oscillation under the state saturation arithmetic and this approach has the advantage of being free from auxiliary parameters as an application the obtained result is applied to the stability analysis of two dimensional dynamics numerical examples are given to illustrate the results

stationary isothermic surfaces and uniformly dense domains we establish a relationship between stationary isothermic surfaces and uniformly dense domains a stationary isothermic surface is a level surface of temperature which does not evolve with time a domain in the n dimensional euclidean space r n is said to be uniformly dense in a surface r n of codimension 1 if for every small r 0 the volume of the intersection of with a ball of radius r and center x does not depend on x for x we prove that the boundary of every uniformly dense domain which is bounded or whose complement is bounded must be a sphere we then examine a uniformly dense domain with unbounded boundary and we show that the principal curvatures of satisfy certain identities the case in which the surface coincides with is particularly interesting in fact we show that if the boundary of a uniformly dense domain is connected then i if n 2 it must be either a circle or a straight line and ii if n 3 it must be either a sphere a spherical cylinder or a minimal surface we conclude with a discussion on uniformly dense domains whose boundary is a minimal surface

the geometry of minimal surfaces of finite genus i curvature estimates and quasiperiodicity let mathcal m be the space of properly embedded minimal surfaces in 3 with genus zero and two limit ends normalized so that every surface m mathcal m has horizontal limit tangent plane at infinity and the vertical component of its flux equals one we prove that if a sequence m i i mathcal m has the horizontal part of the flux bounded from above then the gaussian curvature of the sequence is uniformly bounded this curvature estimate yields compactness results and the techniques in its proof lead to a number of consequences concerning the geometry of any properly embedded minimal surface in 3 with finite genus and the possible limits through a blowing up process on the scale of curvature of a sequence of properly embedded minimal surfaces with locally bounded genus in a homogeneously regular riemannian 3 manifold

technical communique stability analysis of a class of digital filters utilizing single saturation nonlinearity a novel criterion for the global asymptotic stability of a class of digital filters utilizing single saturation nonlinearity is presented an example showing the effectiveness of the present criterion is given

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

the classification of doubly periodic minimal tori with parallel ends let k be the space of properly embedded minimal tori in quotients of r 3 by two independent translations with any fixed even number of parallel ends after an appropriate normalization we prove that k is a 3 dimensional real analytic manifold that reduces to the finite coverings of the examples defined by karcher meeks and rosenberg in 9 10 15 the degenerate limits of surfaces in k are the catenoid the helicoid and three 1 parameter families of surfaces the simply and doubly periodic scherk minimal surfaces and the riemann minimal examples

novel criterion for stability of discrete time systems in a state space realization utilizing saturation nonlinearities abstract a new criterion for the global asymptotic stability of discrete time systems in a state space realization utilizing saturation nonlinearities is presented the form of the criterion is unconventional in that it offers the flexibility of using even an unsymmetric lyapunov matrix p a recently reported criterion is shown to be a special case of the present criterion an example shows the effectiveness of the new criterion

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

hermite polynomials and helicoidal minimal surfaces the main objective of this paper is to construct smooth 1 parameter families of embedded minimal surfaces in euclidean space that are invariant under a screw motion and are asymptotic to the helicoid some of these families are significant because they generalize the screw motion invariant helicoid with handles and thus suggest a pathway to the construction of higher genus helicoids as a byproduct we are able to relate limits of minimal surface families to the zero sets of hermite polynomials

stability analysis for digital filters with multiple saturation nonlinearities a new stability criterion for digital filters with multiple saturation nonlinearities is presented in the form of a linear matrix inequality numerical examples are given to show the effectiveness of the results obtained

stability criterion for a class of fixed point digital filters using two s complement arithmetic a new stability criterion for a class of digital filters using two s complement arithmetic is presented the effectiveness of the obtained results is shown by using a numerical example

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

minimal surfaces with the area growth of two planes the case of infinite symmetry we prove that a connected properly immersed minimal surface in with infinite symmetry group and area growth constant less than is a plane a catenoid or a scherk singly periodic minimal surface as a consequence the scherk minimal surfaces are the only connected periodic minimal desingularizations of the intersections of two planes

variations on a theme of heine and stieltjes an electrostatic interpretation of the zeros of certain polynomials we show a way to adapt the ideas of stieltjes to obtain an electrostatic interpretation of the zeroes of a large class of orthogonal polynomials

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

the classification of singly periodic minimal surfaces with genus zero and scherk type ends given an integer k 2 let s k be the space of complete embedded singly periodic minimal surfaces in r 3 which in the quotient have genus zero and 2k scherk type ends surfaces in s k can be proven to be proper a condition under which the asymptotic geometry of the surfaces is well known it is also known that s 2 consists of the 1 parameter family of singly periodic scherk minimal surfaces we prove that for each k 3 there exists a natural one to one correspondence between s k and the space of convex unitary nonspecial polygons through the map which assigns to each m s k the polygon whose edges are the flux vectors at the ends of m a special polygon is a parallelogram with two sides of length 1 and two sides of length k 1 as consequence s k reduces to the saddle towers constructed by karcher

a limit method for solving period problems on minimal surfaces we introduce a new technique to solve period problems on minimal surfaces called limit method if a family of surfaces has weierstras data converging to the data of a known example and this presents a transversal solution of periods then the original family contains a sub family with closed periods

non periodic riemann examples with handles we show the existence of 1 parameter families of non periodic complete embedded minimal surfaces in euclidean space with infinitely many parallel planar ends in particular we are able to produce finite genus examples and quasi periodic examples of infinite genus

on the genus of triply periodic minimal surfaces we prove the existence of embedded minimal surfaces of arbitrary genus g 3 in any at 3 torus in fact we construct a sequence of such surfaces converging to a planar foliation of the 3 torus in particular the area of the surface can be chosen arbitrarily large

the geometry of minimal surfaces of finite genus ii nonexistence of one limit end examples we demonstrate that a properly embedded minimal surface in 3 with finite genus cannot have one limit end

handle addition for doubly periodic scherk surfaces we prove the existence of a family of embedded doubly periodic minimal surfaces of quotient genus g with orthogonal ends that generalizes the classical doubly periodic surface of scherk and the genus one scherk surface of karcher the proof of the family of immersed surfaces is by induction on genus while the proof of embeddedness is by the conjugate plateau method

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

brief analysis of discrete time piecewise affine and hybrid systems in this paper we present various algorithms both for stability and performance analysis of discrete time piece wise affine pwa systems for stability different classes of lyapunov functions are considered and it is shown how to compute them through linear matrix inequalities that take into account the switching structure of the systems we also show that the continuity of the lyapunov function is not required in discrete time moreover the tradeoff between the degree of conservativeness and computational requirements is discussed finally by using arguments from the dissipativity theory for nonlinear systems we generalize our approach to analyze the l 2 gain of pwa systems

technical communique elimination of overflow oscillations in direct form digital filters using saturation arithmetic a novel frequency domain criterion for the elimination of limit cycles in a class of digital filters using saturation arithmetic is presented an example showing the effectiveness of the present criterion is given