L'équation de la chaleur associée à la courbure de Ricci
Les équations de Hua d'un domaine borné symétrique du type tube.
Les inégalités de Morse
Les singularités des fonctions spectrales sur une variété riemannienne infiniment aplatie
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.
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
Lie Groups and KdV Equations.
Lie symmetries analysis of the shallow water equations.
Limiting angle of brownian motion in certain two-dimensional Cartan-Hadamard manifolds
Limiting behaviors of the Brownian motions on hyperbolic spaces
Using explicit representations of the Brownian motions on hyperbolic spaces, we show that their almost sure convergence and the central limit theorems for the radial components as time tends to infinity can be easily obtained. We also give a straightforward strategy to obtain explicit expressions for the limit distributions or Poisson kernels.
L'inégalité de Penrose
Liouville theorem for harmonic maps with potential.
Liouville type theorems for some conformally invariant fully nonlinear equations
This is a report on some joint work with Aobing Li on Liouville type theorems for some conformally invariant fully nonlinear equations.
Liouville type theorems for φ-subharmonic functions.
In this paper we present some Liouville type theorems for solutions of differential inequalities involving the φ-Laplacian. Our results, in particular, improve and generalize known results for the Laplacian and the p-Laplacian, and are new even in these cases. Phragmen-Lindeloff type results, and a weak form of the Omori-Yau maximum principle are also discussed.
Liouville's theorem for first-order partial differential operators
Littlewood-Paley decompositions on manifolds with ends
For certain non compact Riemannian manifolds with ends which may or may not satisfy the doubling condition on the volume of geodesic balls, we obtain Littlewood-Paley type estimates on (weighted) spaces, using the usual square function defined by a dyadic partition.
Littlewood-Paley-Stein functions on complete Riemannian manifolds for 1 ≤ p ≤ 2
We study the weak type (1,1) and the -boundedness, 1 < p ≤ 2, of the so-called vertical (i.e. involving space derivatives) Littlewood-Paley-Stein functions and ℋ respectively associated with the Poisson semigroup and the heat semigroup on a complete Riemannian manifold M. Without any assumption on M, we observe that and ℋ are bounded in , 1 < p ≤ 2. We also consider modified Littlewood-Paley-Stein functions that take into account the positivity of the bottom of the spectrum. Assuming that...
Ljusternik-Schnirelmann theory on -manifolds