Stochastic completeness and volume growth

DOI10.1090/S0002-9939-10-10281-0zbMath1201.58024arXiv0908.4222MaRDI QIDQ3574838

Christian Bär, Gregório Pacelli Bessa

Publication date: 2 July 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.4222

zbMATH Keywords

Brownian motionRiemannian manifoldheat kernelvolume growthstochastic completeness

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (9)

Volume growth, spectrum and stochastic completeness of infinite graphs ⋮ On the \(L ^{1}\)-Liouville property of stochastically incomplete manifolds ⋮ A note on the triviality of gradient solitons of the Ricci-Bourguignon flow ⋮ The \(L^1\)-Liouville property on graphs ⋮ Stochastically complete, parabolic and \(L^1\)-Liouville spacelike submanifolds with parallel mean curvature vector ⋮ A note on the volume growth criterion for stochastic completeness of weighted graphs ⋮ Spectral and stochastic properties of the \(f\)-Laplacian, solutions of PDEs at infinity and geometric applications ⋮ Dirichlet parabolicity and \(\mathsf{L}^{1}\)-Liouville property under localized geometric conditions ⋮ Stochastic incompleteness for graphs and weak Omori-Yau maximum principle

Cites Work

• Function theory, random paths and covering spaces
• Harmonic functions on complete riemannian manifolds
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Maximum principles on Riemannian manifolds and applications
• A remark on the maximum principle and stochastic completeness
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