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arXiv · 1109.3380

Stochastic Properties of the Laplacian on Riemannian Submersions

M. Cristiane Brandão·Jobson Q. Oliveira
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Abstract

Based on ideas of Pigolla and Setti \cite{PS} we prove that immersed submanifolds with bounded mean curvature of Cartan-Hadamard manifolds are Feller. We also consider Riemannian submersions $π\colon M \to N$ with compact minimal fibers, and based on various criteria for parabolicity and stochastic completeness, see \cite{Grygor'yan}, we prove that $M$ is Feller, parabolic or stochastically complete if and only if the base $N$ is Feller, parabolic or stochastically complete respectively.

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M. Cristiane Brandão, Jobson Q. Oliveira. 2011-09-15. Stochastic Properties of the Laplacian on Riemannian Submersions. https://arxiv.org/abs/1109.3380

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