Generalized maximum principles and stochastic completeness for pseudo-Hermitian manifolds

TL;DR

This paper develops a generalized maximum principle for pseudo-Hermitian manifolds, linking it to stochastic completeness and providing new applications in geometric analysis.

Contribution

It introduces a generalized maximum principle for pseudo-Hermitian manifolds and establishes its equivalence with stochastic completeness, extending classical results to this setting.

Findings

Omori-Yau maximum principles derived for pseudo-Hermitian manifolds

Stochastic completeness equivalent to a weak maximum principle

Applications demonstrating the utility of the generalized maximum principles

Abstract

In this paper, we establish a generalized maximum principle for pseudo-Hermitian manifolds. As corollaries, Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced. Moreover, we 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, we give some applications of these generalized maximum principles.