Géométrie différentielle du 2ème ordre, semi-martingales et équations différentielles stochastiques sur une variété différentielle
Géométrie différentielle stochastique, II
Géométrie stochastique sans larmes, I
Geometry of non-holonomic diffusion
We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For -Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard.
Geometry of stochastic delay differential equations.
Geometry of the Complex Homogeneous Monge-Ampère Equation.
Germes de configurations legendriennes stables et fonctions d'Airy-Weber généralisées
On sait depuis Maslov, Arnold, etc... associer à presque tout germe de variété lagrangienne ou legendrienne lisse une classe de fonctions oscillantes qui sous des hypothèses génériques à la Thom fournissent des modèles universels pour le comportement d’une onde lumineuse au voisinage de la caustique.Le présent article étend cette construction à une classe de situations où la variété caractéristique est un germe singulier (union de composantes lisses), qui peut néanmoins être stable en ce sens que...
-invariant variational principles on frame bundles.
Global existence for a nonlinear Schroedinger–Chern–Simons system on a surface
Global existence of solutions to Schrödinger equations on compact riemannian manifolds below
In this paper, we will study global well-posedness for the cubic defocusing nonlinear Schrödinger equations on the compact Riemannian manifold without boundary, below the energy space, i.e. , under some bilinear Strichartz assumption. We will find some , such that the solution is global for .
Global existence theorems for hyperbolic harmonic maps
Global Real Analyticity of Solutions to the ...-Neumann Problem.
Global solution of the wave equation
Global solvability for certain classes of underdetermined systems of vector fields.
Global weak solutions for dimensional wave maps into homogeneous spaces
Gradient estimates for a nonlinear equation on complete noncompact manifolds
Let be a complete noncompact Riemannian manifold. We consider gradient estimates on positive solutions to the following nonlinear equation in , where , are two real constants and , is a smooth real valued function on and . When is finite and the -Bakry-Emery Ricci tensor is bounded from below, we obtain a gradient estimate for positive solutions of the above equation. Moreover, under the assumption that -Bakry-Emery Ricci tensor is bounded from below and is bounded from above,...
Gradient estimates for inverse curvature flows in hyperbolic space
We prove gradient estimates for hypersurfaces in the hyperbolic space Hn+1, expanding by negative powers of a certain class of homogeneous curvature functions F. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers p > 1 of F-1 and smooth convergence of the properly rescaled hypersurfaces. In particular, the full convergence result holds for the inverse Gauss curvature flow of surfaces without any further pinching condition besides convexity of the initial hypersurface....
Gradient estimates, Harnack inequalities and estimates for heat kernels of the sum of squares of vector fields.
Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds
In this paper, we consider gradient estimates on complete noncompact Riemannian manifolds for the following general heat equation where is a constant and is a differentiable function defined on . We suppose that the Bakry-Émery curvature and the -dimensional Bakry-Émery curvature are bounded from below, respectively. Then we obtain the gradient estimate of Li-Yau type for the above general heat equation. Our results generalize the work of Huang-Ma ([4]) and Y. Li ([6]), recently.
Grafting Seiberg-Witten monopoles.