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Associative and Lie deformations of Poisson algebras

Elisabeth Remm (2012)

Communications in Mathematics

Considering a Poisson algebra as a nonassociative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this nonassociative algebra. We give a natural interpretation of deformations which preserve the underlying associative structure and of deformations which preserve the underlying Lie algebra and we compare the associated cohomologies with the Poisson cohomology parametrizing the general deformations of Poisson algebras.

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...

Currently displaying 741 – 760 of 776