Récurrence et généricité

Résumé. Nous montrons un lemme de connexion C¹ pour les pseudo-orbites des difféomorphismes des variétés compactes. Nous explorons alors les conséquences pour les difféomorphismes C¹-génériques. Par exemple, les difféomorphismes conservatifs C¹-génériques (dune variété connexe) sont transitifs.

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We prove a C¹-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C¹-generic diffeomorphisms. For instance, C¹-generic conservative diffeomorphisms (on connected manifolds) are transitive.

     

Dérivée et primitive aréolaires

Résumé En définissant la notion de primitive aréolaire, on étudie à ce point de vue les fonctions holomorphes (α) et les fonctions monogènes (α) introduites par l'auteur, ainsi que les sapports entre ces fonctions et les fonctions de la classe et les -primitives selon I. N. Vekua. à Giovanni Sansone pour son 70^me anniversaire.     

Inégalités de Brascamp-Lieb et convexité

This note gives an elementary proof of an inequality of Brascamp-Lieb and of a new dual inequality that has numerous applications to convexity: lower estimates of volumes of projections, of exterior volume ratio and MM^* -estimate in the non symmetric case.     

Moyennes limites et convexité

SoitF l'ensemble des fonctions bornées, définies surR ₊, à valeurs réelles non négatives, dont l'intégrale au sens de Lebesgue existe localement. A une fonctiona deF on associe le coupleL(a) des limites supérieure et inférieure de , quandt tend vers +. On pose

Géométrie spectrale et formules d'indices locales pour les variétés CR et contact

We present here geometric applications of the non-commutative residue for Heisenberg manifolds. Thereby we obtain conformal invariants, we define the area of a pseudo-Hermitian manifolds and we derive local formulae for the index of some sub-elliptic operators.     

Croissance lineaire et géométrie bornée

We show that on a noncompact manifold which has finite topology at infinity, there exists a Riemannian metric with bounded geometry and linear growth-type.     

Ondes et radiations électromagnétiques et gravitationelles en relativité générale

Résumé Théorie des ondes et radiations gravitationelles basée sur l’analogie existant entre les comportements du tenseur de courbure et du tenseur champ électromagnétique en relativité générale. Contribution à la quantification des champs. à Antonio Signorini pour son 70^me anniversaire.     

Ombres Convexité, régularité et sous-harmonicité

Letf:V→R be a function defined on a subsetV ofR ⁿ ×R ^d let?:x→inf{f(x t);t such that(x t)∈V} denote theshadow off and letΦ={(x t)∈V; f(x t)=?(x)} This paper deals with the characterization of some properties of ? in terms of the infinitesimal behavior off near points ζ∈Φ proving in particular a conjecture of J M Trépreau concerning the cased=1 Characterizations of this type are provided for the convexity the subharmonicity or theC ^{1 1} regularity of ? in the interior ofI={x∈ R ⁿ;εR ^d (x t)∈V} and in theC ^{1 1} case an expression forD ²? is given To some extent an answer is given to the following question: which convex function ?:I→R I interval ?R (resp which function √:I→R of classC ^{1 1}) is the shadow of aC ² functionf:I×R→R?     

Courbure intégrale généralisée et homotopie

Sans résumé     

Singularités canoniques et actions horosphériques

Let G be a connected reductive linear algebraic group. We consider the normal G-varieties with horospherical orbits. In this short note, we provide a criterion to determine whether these varieties have at most canonical, log canonical or terminal singularities in the case where they admit an algebraic curve as rational quotient. This result seems to be new in the special setting of torus actions with general orbits of codimension 1. For the given G-variety X, our criterion is expressed in terms of a weight function ${\omega }_X$ that is constructed from the set of G-invariant valuations of the function field $k(X)$. In the log terminal case, the generating function of ${\omega }_X$ coincides with the stringy motivic volume of X. As an application, we discuss the case of normal $k^{?}$-surfaces.     

Géométrie diophantienne et variétés toriques

We present some results on projective toric varieties which are relevant in diophantine geometry. We interpret and study several invariants attached to these varieties by geometrical and combinatorial terms. We also give a Bézout theorem for Chow weights of projective varieties and an application to the theorem of successive algebraic minima. These results are extracted from the two texts of Philippon and Sombra mentioned in the references at the end of this Note (both downloadable from http://fr.arxiv.org). To cite this article: P. Philippon, M. Sombra, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Transplantation et isospectralité. I

Sans résumé

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Recherche effectuée au sein de l'U.R.A. C.N.R.S. n^o 188 et qui a bénéficié de crédits du contrat CEE#SC 1-0105-C GADGET et de l'OTAN     

Convexes Hyperboliques et Quasiisométries

For any m ≥ 3, we construct properly convex open sets Ω in the real projective space whose Hilbert metric is Gromov hyperbolic but is not quasiisometric to the hyperbolic space . We show that such examples cannot exist for m = 2. Some of our examples are divisible, i.e. there exists a discrete group Г of projective transformations preserving Ω with a compact quotient Г\Ω. The open set Ω is strictly convex but the group Г is not isomorphic to any cocompact lattice in the isometry group of .     

Réduction symplectique et quantification

We present a direct analytic proof of the Guillemin-Sternberg geometric quantization conjecture [2]. Further extensions are also obtained.     

Graphes arithmétiques et syzygies

We give an effective method to find the numerical information of the minimal free resolution of an arithmetically Cohen-Macaulay projective curve using an arithmetic graph easily build from the exponents defining the curve.     

Linéarisation et maillage des surfaces paramétrées

We propose a methodology to simplify the parameterization of a surface composed of parametric patches, typically encountered in CAD (computer aided design) environments. This new parameterization is defined via the construction of an adaptive triangulation, called support, of each patch. The adaptation is governed by the control of the gap between the initial parameterization of the patch and that of the support. This support is used to generate the mesh of the CAD surface using an indirect approach, in which the mesh is generated via the parametric domains. The support makes it possible to disconnect the mesher from the CAD system, and in this sense it constitutes a universal tool for meshing such surfaces. An application example is given to show the pertinency of our methodology.     

Catégories dérivées et variétés de Deligne-Lusztig

Sans résumé