Generalized Maximum Principles and Stochastic Completeness for Pseudo-Hermitian Manifolds

Abstract

In this paper, the authors establish a generalized maximum principle for pseudo-Hermitian manifolds. As corollaries, Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced. Moreover, they prove that the stochastic completeness for the heat semigroup generated by the sub-Laplacian is equivalent to the validity of a weak form of the generalized maximum principles. Finally, they give some applications of these generalized maximum principles.

Keywords

Pseudo-Hermitian manifold / Omori-Yau type maximum principles / Stochastic completeness

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