sequences of willmore surfaces in this paper we develop the theory of willmore sequences for willmore surfaces in the 4 sphere we show that under appropriate conditions this sequence has to terminate in this case the willmore surface either is the twistor projection of a holomorphic curve into mathbb c mathbb p 3 or the inversion of a minimal surface with planar ends in mathbb r 4 these results give a unified explanation of previous work on the characterization of willmore spheres and willmore tori with non trivial normal bundles by various authors

partial persistence and extinction in n dimensional competitive systems abstract in this paper we first consider an n dimensional system slightly more general than the lotka volterra system and give conditions that imply strong persistence of all species using this result we then give computable conditions on the coefficients which imply the ultimate extinction of certain species in an n dimensional lotka volterra system

surfaces immersed in lie algebras obtained from the sigma models we study some geometrical aspects of two dimensional orientable surfaces arising from the study of sigma models to this aim we employ an identification of with the lie algebra by means of which we construct a generalized weierstrass formula for immersion of such surfaces the structural elements of the surface like its moving frame the gauss weingarten and the gauss codazzi ricci equations are expressed in terms of the solution of the model defining it further the first and second fundamental forms the gaussian curvature the mean curvature vector the willmore functional and the topological charge of surfaces are expressed in terms of this solution we present detailed implementation of these results for surfaces immersed in and lie algebras

lawson s genus two surface and meromorphic connections we investigate the lawson genus 2 surface by methods from integrable system theory to this surface we derive a globally defined meromorphic dpw potential which is determined up to two unknown functions depending only on the spectral parameter

the geometric complexity of special lagrangian t2 cones we prove a number of results on the geometric complexity of special lagrangian slg t2 cones in 3 every slg t2 cone has a fundamental integer invariant its spectral curve genus we prove that the spectral curve genus of an slg t2 cone gives a lower bound for its geometric complexity i e the area the stability index and the legendrian index of any slg t2 cone are all bounded below by explicit linearly growing functions of the spectral curve genus we prove that the cone on the clifford torus which has spectral curve genus zero in s5 is the unique slg t2 cone with the smallest possible legendrian index and hence that it is the unique stable slg t2 cone this leads to a classification of all rigid index 1 slg cone types in dimension three for cones with spectral curve genus two we give refined lower bounds for the area the legendrian index and the stability index one consequence of these bounds is that there exist s1 invariant slg torus cones of arbitrarily large area legendrian and stability indices we explain some consequences of our results for the programme due to joyce to understand the most common three dimensional isolated singularities of generic families of slg submanifolds in almost calabi yau manifolds

a hopf differential for constant mean curvature surfaces in s2 r and h2 r a basic tool in the theory of constant mean curvature cmc surfaces in space forms is the holomorphic quadratic differential discovered by h hopf in this paper we generalize this differential to immersed cmc surfaces in the product spaces s r and h r and prove a corresponding result about the geometry of immersed cmc spheres s in these target spaces

oscillations and limit cycles in lotka volterra systems with delays abstract in this paper competitive lotka volterra systems are studied that have distributed delays and constant coefficients on interaction terms and have time dependent growth rate vectors with an asymptotically constant average algebraic conditions are found to rule out non vanishing oscillations for such systems and heteroclinic limit cycles for autonomous systems as a supplement to these results simple sufficient conditions are provided for certain components of all solutions to vanish and a criterion is given for partial permanence an outstanding feature of all these results is that the conditions are irrelevant of the size and distribution of the delays

the geometry of real sine gordon wavetrains the characterization ofreal n phase quasiperiodic solutions of the sine gordon equation has been an open problem in this paper we achieve this result employing techniques of classical algebraic geometry which have not previously been exploited in the soliton literature a significant by product of this approach is a naturalalgebraic representation of the full complex isospectral manifolds and an understanding of how the real isospectral manifolds are embedded by placing the problem in this general context these methods apply directly to all soliton equations whose multiphase solutions are related to hyperelliptic functions

deformations of surfaces associated with integrable gauss mainardi codazzi equations using the formulation of the immersion of a two dimensional surface into the three dimensional euclidean space proposed recently a mapping from each symmetry of integrable equations to surfaces in r3 can be established we show that among these surfaces the sphere plays a unique role indeed under the rigid su 2 rotations all integrable equations are mapped to a sphere furthermore we prove that all compact surfaces generated by the infinitely many generalized symmetries of the sine gordon equation are homeomorphic to a sphere we also find some new weingarten surfaces arising from the deformations of the modified kurteweg de vries and of the nonlinear schrodinger equations surfaces can also be associated with the motion of curves we study curve motions on a sphere and we identify a new integrable equation characterizing such a motion for a particular choice of the curve velocity

average growth and extinction in a competitive lotka volterra system abstract in this paper we answer an earlier conjecture consider a class of nonautonomous competitive lotka volterra systems we show that certain inequalities involving the interaction coefficients and averages of the growth rates imply that the system is persistent however reversing one of these inequalities implies that the n th species goes to extinction

average conditions for permanence and extinction in nonautonomous lotka volterra system abstract an n species nonautonomous competitive lotka volterra system is considered in this paper the average conditions on the coefficients are given to guarantee that all but one of the species are driven to extinction the generalization for the result is presented that is for each r n the average conditions on the coefficients are provided to guarantee that r of the species in the system are permanent while the remaining n r are driven to extinction it is shown that these average conditions are improvement of those of ahmad and montes de oca appl math comput 90 1998 155 166 and montes de oca and zeeman proc amer math soc 124 1996 3677 3687 and j math anal appl 192 1995 360 370

vanishing components in autonomous competitive lotka volterra systems abstract sufficient conditions are found for an n dimensional autonomous competitive lotka volterra system to have a component vanishing in an exponential rate as t these conditions incorporate a typical known result in the literature as a particular case moreover if the n dimensional system degenerates asymptotically to an m dimensional subsystem as t then under these conditions on the subsystem the property that the ith component of every solution of the subsystem vanishes in an exponential rate is also preserved for the n dimensional system

embedded constant mean curvature tori in the three sphere we prove that any constant mean curvature embedded torus in the three dimensional sphere is axially symmetric and use this to give a complete classification of such surfaces for any given value of the mean curvature

flows of constant mean curvature tori in the 3 sphere the equivariant case we present a deformation for constant mean curvature tori in the 3 sphere we show that the moduli space of equivariant constant mean curvature tori in the 3 sphere is connected and we classify the minimal the embedded and the alexandrov embedded tori therein

archimedean zeta integrals on u 2 1 it is known that for a dual pair of unitary groups with equal size zeta integrals arising from rallis inner product formula give the central values of certain au tomorphic l functions which have applications to arithmetic in this paper we explicitly calculate archimedean zeta integrals of this type for u 2 1 in particular we compute the matrix coefficients of weil representations using joint harmonics in the fock model and those of discrete series using schmid operators in the theory of automorphic forms to obtain deep arithmetic applications it is often necessary to have effectively computable results locally at each place of a number field in particular at archimedean places we need some detailed calculations on the harmonic analysis of real lie groups and have to face certain combinatorial complexity in l1 l2 the author works out the local archimedean theory for cohomological rep resentations and the connection to special values of l functions in the stable range the local theory of theta correspondence for unitary groups is developed in hks for p adic fields and in p for field of real numbers it is made more precise in h1 h2 and applied to obtain results about special values of l functions the article hls outlines the general global theory of theta correspondence for cuspidal automorphic representations of unitary groups in which the authors obtain a general formula for the local zeta integral on unitary groups and show that the central l value is non negative we shall explain the motivation and background of this paper by a brief review for above context following hls let f be a totally real number field f a totally imaginary quadratic extension of f a a f the adele ring of f let v resp v be a hermitian resp skew hermitian vector space of dimension n over f and w v f v a symplectic space over f fixing an additive character and a complete polarization w x y we have the schrodinger model of the oscillator representation of f sp w a realized on the space s x a of schwartz bruhat functions on x a let g u v g u v by choosing a global splitting character of a f cf hls then defines a weil representation v v of g a g a on s x a as usual for s x a we have the theta kernel g g x x f