Poincare inequality and the uniqueness of solutions for the heat equation associated with subelliptic diffusion operators
arXiv:1305.0508
Abstract
In this paper we study global Poincare inequalities on balls in a large class of sub-Riemannian manifolds satisfying the generalized curvature dimension inequality introduced by F.Baudoin and N.Garofalo. As a corollary, we prove the uniqueness of solutions for the subelliptic heat equation. Our results apply in particular to CR Sasakian manifolds with Tanaka-Webster-Ricci curvature bounded from below and Carnot groups of step two.
References in corpus (5)
- Widder's representation theorem for symmetric local Dirichlet spaces
- A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality
- Sobolev, Poincare and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality
- Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds
- Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry