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arXiv · 1305.0508

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

Bumsik Kim
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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.

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Bumsik Kim. 2013-05-02. Poincare inequality and the uniqueness of solutions for the heat equation associated with subelliptic diffusion operators. https://arxiv.org/abs/1305.0508

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