PARABOLIC HARNACK INEQUALITY ON METRIC SPACES WITH A GENERALIZED VOLUME PROPERTY

GIACOMO DE LEVA

doi:10.2748/tmj/1318338945

Tohoku Mathematical Journal, Second Series

Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735

PARABOLIC HARNACK INEQUALITY ON METRIC SPACES WITH A GENERALIZED VOLUME PROPERTY

GIACOMO DE LEVA

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Keywords: Alexandrov space, infinitesimal Bishop-Gromov condition, parabolic Harnack inequality, heat kernel, harmonic functions, subharmonic functions

JOURNAL FREE ACCESS

2011 Volume 63 Issue 3 Pages 303-327

DOI https://doi.org/10.2748/tmj/1318338945

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Abstract

We study the parabolic Harnack inequality on metric measure spaces with the more general volume growth property than the volume doubling property. As applications we extend some Liouville theorems and heat kernel estimates for Riemannian manifolds to Alexandrov spaces satisfying a volume comparison condition of Bishop-Gromov type.

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