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Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature

Shigetoshi Yazaki (2007)

Kybernetika

Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex:...

Asymptotic behaviour and the moduli space of doubly-periodic instantons

Olivier Biquard, Marcos Jardim (2001)

Journal of the European Mathematical Society

We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus T with a complex line ℂ , with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to T × ℙ 1 . The converse statement is also true, namely a holomorphic bundle on T × ℙ 1 which is flat on the torus at infinity, and satisfies a stability condition, comes from a doubly-periodic instanton....

Asymptotic isoperimetry of balls in metric measure spaces.

Romain Tessera (2006)

Publicacions Matemàtiques

In this paper, we study the asymptotic behavior of the volume of spheres in metric measure spaces. We first introduce a general setting adapted to the study of asymptotic isoperimetry in a general class of a metric measure space...

Asymptotic values of minimal graphs in a disc

Pascal Collin, Harold Rosenberg (2010)

Annales de l’institut Fourier

We consider solutions of the prescribed mean curvature equation in the open unit disc of euclidean n-dimensional space. We prove that such a solution has radial limits almost everywhere; which may be infinite. We give an example of a solution to the minimal surface equation that has finite radial limits on a set of measure zero, in dimension two. This answers a question of Nitsche.

Asymptotic windings over the trefoil knot.

Jacques Franchi (2005)

Revista Matemática Iberoamericana

Consider the group G:=PSL2(R) and its subgroups Γ:= PSL2(Z) and Γ':=DSL2(Z). G/Γ is a canonical realization (up to an homeomorphism) of the complement S3T of the trefoil knot T, and G/Γ' is a canonical realization of the 6-fold branched cyclic cover of S3T, which has a 3-dimensional cohomology of 1-forms.Putting natural left-invariant Riemannian metrics on G, it makes sense to ask which is the asymptotic homology performed by the Brownian motion in G/Γ', describing thereby in an intrinsic way part...

Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles

Robert Berman, Johannes Sjöstrand (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we obtain the full asymptotic expansion of the Bergman-Hodge kernel associated to a high power of a holomorphic line bundle with non-degenerate curvature. We also explore some relations with asymptotic holomorphic sections on symplectic manifolds.

Atoroïdalité complète et annulation de l’invariant λ ¯ de Perelman

Pablo Suárez-Serrato (2007/2008)

Séminaire de théorie spectrale et géométrie

On résume les proprietés de l’invariant λ ¯ de Perelman, et en combinaison avec l’invariant de Yamabe on exprime certaines proprietés géométriques des variétés de dimension 3 en fonction de λ ¯ . On décrit des exemples d’annulation de λ ¯ en dimension 4 , où on trouve des liens entre l’effondrement et l’existence de métriques à courbure scalaire positive. On montre qu’une version d’atoroïdalité qu’on appelle atoroïdalité complète est détectée par λ ¯ sur les variétés de courbure négative ou nulle de dimension...

Au bord de certains polyèdres hyperboliques

Marc Bourdon (1995)

Annales de l'institut Fourier

Le cadre de cet article est celui des groupes et des espaces hyperboliques de M.  Gromov. Il est motivé par la question suivante : comment différencier deux groupes hyperboliques à quasi-isométrie près ? On illustre ce problème en détaillant un exemple de M. Gromov issu de Asymptotic invariants for infinite groups. On décrit une famille infinie de groupes hyperboliques, deux à deux non quasi-isométriques, de bord la courbe de Menger. La méthode consiste à étudier leur structure quasi-conforme au...

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