Stochastic Properties of the Laplacian on Riemannian Submersions

Details Stochastic Properties of the Laplacian on Riemannian Submersions Stochastic Properties of the Laplacian on Riemannian Submersions

2011-09-15

arxiv.org/abs/1109.3380v1

Mathematics

Differential Geometry

Scientific paper

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 $\pi \colon M \to N$ 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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