Stochastic Properties of the Laplacian on Riemannian Submersions

2011/09/15 by Brandão, M. Cristiane, Oliveira, Jobson Q.
#53C25 #58G11 #58J65 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.3380

Abstract

Based on ideas of Pigolla and Setti \citePS we prove that immersed submanifolds with bounded mean curvature of Cartan-Hadamard manifolds are Feller. We also consider Riemannian submersions π\colon M → N with compact minimal fibers, and based on various criteria for parabolicity and stochastic completeness, see \citeGrygor'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.

Related

• On stochastically complete submanifolds
• The Feller property on Riemannian manifolds
• Qualitative properties of bounded subsolutions of nonlinear PDEs
• Comparison principle, stochastic completeness and half-space theorems
• Moment estimates for the stochastic heat equation on Cartan-Hadamard manifolds