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 $C^{0}$-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.

The Feller property on Riemannian manifolds

PIGOLA, STEFANO;SETTI, ALBERTO GIULIO
2012-01-01

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 $C^{0}$-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.
2012
Pigola, Stefano; Setti, ALBERTO GIULIO
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1735931
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