Poincare inequality and the uniqueness of solutions for the heat equation associated with subelliptic diffusion operators

2013/05/02 by Bumsik Kim, Kim, Bumsik · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Probability (math.PR) #math.AP #math.DG #math.FA #math.PR

paper · pdf · doi:10.48550/arxiv.1305.0508

arxiv created 2013/05/02 · openalex publication_date 2013/05/02 · arxiv updated 2013/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds
• Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds

Cited by

• On Liouville-type theorems and the uniqueness of the positive Cauchy problem for a class of hypoelliptic operators

Related

• Sobolev, Poincare and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality
• Heat kernel upper bounds under the generalized curvature(-dimension) inequality
• Subelliptic Li-Yau estimates on three dimensional model spaces
• Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries
• Curvature dimension inequalities and subelliptic heat kernel gradient bounds on contact manifolds