The Feller property on Riemannian manifolds

2010/10/08 by Stefano Pigola, Pigola, Stefano, Alberto G. Setti +1 · 1 citation
Mathematics · #31B35 #58J05 #58J35 #58J65 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1010.1653

openalex publication_date 2010/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The asymptotic behavior of the heat kernel of a Riemannian manifold gives rise to the classical concepts of parabolicity, stochastic completeness (or conservative property) and Feller property (or C⁰-diffusion property). Both parabolicity and stochastic completeness have been the subject of a systematic study which led to discovering not only sharp geometric conditions for their validity but also an incredible rich family of tools, techniques and equivalent concepts ranging from maximum principles at infinity, function theoretic tests (Khas'minskii criterion), comparison techniques etc... The present paper aims to move a number of steps forward in the development of a similar apparatus for the Feller property.

Cited by

• Form uniqueness for graphs with weakly spherically symmetric ends

Related

• Stochastic Properties of the Laplacian on Riemannian Submersions
• Coverings and the heat equation on graphs: stochastic incompleteness, the Feller property and uniform transience
• A note on the strong Feller property of diffusion processes
• Qualitative properties of bounded subsolutions of nonlinear PDEs
• Revisiting Feller Diffusion: Derivation and Simulation