Les premiers travaux d’Yves Colin de Verdière
Les singularités des fonctions spectrales sur une variété riemannienne infiniment aplatie
Les travaux de Nabutovsky et Weinberger sur la complexité de l'espace des variétés riemanniennes
Les valeurs propres inférieures à 1/4 des surfaces de Riemann de petit rayon d'injectivité.
Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein.
Les variétés hyperboliques sont des minima locaux de l'entropie topologique.
Levi forms, differential forms of type (0,1) and pseudoconvexity in Banach spaces
Levi's forms of higher codimensional submanifolds
Let , let be a hypersurface of , be a submanifold of . Denote by the Levi form of at . In a previous paper [3] two numbers , are defined; for they are the numbers of positive and negative eigenvalues for . For , , we show here that are still the numbers of positive and negative eigenvalues for when restricted to . Applications to the concentration in degree for microfunctions at the boundary are given.
Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group
Lévy-Gromov's isometric inequality for an infinite dimensional diffusion generator.
Lewy's theorem fails in higher dimensions.
L-homology theory of FSQL-manifolds and the degree of FSQL-mappings
A homology theory of Banach manifolds of a special form, called FSQL-manifolds, is developed, and also a homological degree of FSQL-mappings between FSQL-manifolds is introduced.
Lie algebras connected with associative ones
Lie derivative of vector fields on a differential space
Lie derivatives and natural operators
Lie derivatives of sectorform fields
Lie group extensions associated to projective modules of continuous inverse algebras
We call a unital locally convex algebra a continuous inverse algebra if its unit group is open and inversion is a continuous map. For any smooth action of a, possibly infinite-dimensional, connected Lie group on a continuous inverse algebra by automorphisms and any finitely generated projective right -module , we construct a Lie group extension of by the group of automorphisms of the -module . This Lie group extension is a “non-commutative” version of the group of automorphism...
Lie group structures on groups of diffeomorphisms and applications to CR manifolds
We give general sufficient conditions to guarantee that a given subgroup of the group of diffeomorphisms of a smooth or real-analytic manifold has a compatible Lie group structure. These results, together with recent work concerning jet parametrization and complete systems for CR automorphisms, are then applied to determine when the global CR automorphism group of a CR manifold is a Lie group in an appropriate topology.
Lie groupoids as generalized atlases
Starting with some motivating examples (classical atlases for a manifold, space of leaves of a foliation, group orbits), we propose to view a Lie groupoid as a generalized atlas for the “virtual structure” of its orbit space, the equivalence between atlases being here the smooth Morita equivalence. This “structure” keeps memory of the isotropy groups and of the smoothness as well. To take the smoothness into account, we claim that we can go very far by retaining just a few formal properties of embeddings...
Lie groupoids of mappings taking values in a Lie groupoid
Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are prime examples of infinite-dimensional Lie groups modelled on locally convex spaces. In the present paper, we generalise this construction and show that differentiable mappings on a compact manifold (possibly with boundary) with values in a Lie groupoid form infinite-dimensional Lie groupoids which we...