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Sur une famille de variétés à bord lipschitziennes. Application à un problème d'identification de domaines

Denise Chenais (1977)

Annales de l'institut Fourier

D étant un ouvert borné de R n donné, on considère l’ensemble V L ( r , k ) des ouverts de R n inclus dans D , localement uniformément image de demi-espaces par des homéomorphismes bilipschitiziens. Les cartes locales sont définies sur des boules de rayon r , elles sont bilipschitziennes de constante k .On montre que cette famille est plus générale que celle des ouverts uniformément lipschitziens.On montre ensuite en utilisant une méthode de réflexions que pour Ω ∈ V L ( r , k ) , les espaces de Sobolev W p 1 ( Ω )

Surgery on pairs of closed manifolds

Alberto Cavicchioli, Yuri V. Muranov, Fulvia Spaggiari (2009)

Czechoslovak Mathematical Journal

To apply surgery theory to the problem of classifying pairs of closed manifolds, it is necessary to know the subgroup of the group L P * generated by those elements which are realized by normal maps to a pair of closed manifolds. This closely relates to the surgery problem for a closed manifold and to the computation of the assembly map. In this paper we completely determine such subgroups for many cases of Browder-Livesay pairs of closed manifolds. Moreover, very explicit results are obtained in the...

Symétries spectrales des fonctions zêtas

Frédéric Paugam (2009)

Journal de Théorie des Nombres de Bordeaux

On définit, en réponse à une question de Sarnak dans sa lettre a Bombieri [Sar01], un accouplement symplectique sur l’interprétation spectrale (due à Connes et Meyer) des zéros de la fonction zêta. Cet accouplement donne une formulation purement spectrale de la démonstration de l’équation fonctionnelle due à Tate, Weil et Iwasawa, qui, dans le cas d’une courbe sur un corps fini, correspond à la démonstration géométrique usuelle par utilisation de l’accouplement de dualité de Poincaré Frobenius-équivariant...

Symmetric algebras and Yang-Baxter equation

Beidar, K., Fong, Y., Stolin, A. (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

Let U be an open subset of the complex plane, and let L denote a finite-dimensional complex simple Lie algebra. A. A. Belavin and V. G. Drinfel’d investigated non-degenerate meromorphic functions from U × U into L ⊗ L which are solutions of the classical Yang-Baxter equation [Funct. Anal. Appl. 16, 159-180 (1983; Zbl 0504.22016)]. They found that (up to equivalence) the solutions depend only on the difference of the two variables and that their set of poles forms a discrete (additive) subgroup Γ of the...

Symmetric caustics and Curie's principle

Alain Joets, Ahmed Belaidi, Roland Ribotta (2003)

Banach Center Publications

Physical systems producing caustics may possess symmetries. In that case the relation between the symmetry of the system, considered as a whole, and the symmetry of the caustic follow a very general symmetry principle, the Curie principle. We give various examples of application of the Curie principle to caustics produced by the deflection of light in liquid crystals: the so called squint effect, the visualization of a new type of roll structure, etc. We show also that the Curie principle applies...

Symmetries and currents in nonholonomic mechanics

Michal Čech, Jana Musilová (2014)

Communications in Mathematics

In this paper we derive general equations for constraint Noethertype symmetries of a first order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and effective geometrical theory of nonholonomic constrained systems on fibred manifolds and their jet prolongations, first presented and developed by Olga Rossi. As a representative example of application of the geometrical theory...

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