Parabolic Harnack inequality on metric spaces with a generalized volume property (Q654019)
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scientific article; zbMATH DE number 5991010
| Language | Label | Description | Also known as |
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| English | Parabolic Harnack inequality on metric spaces with a generalized volume property |
scientific article; zbMATH DE number 5991010 |
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Parabolic Harnack inequality on metric spaces with a generalized volume property (English)
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21 December 2011
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In this article, the author establishes a parabolic Harnack inequality in a general setting that contains spaces satisfying a volume comparison condition of Bishop-Gromov type [\textit{K. Kuwae} and \textit{T. Shioya}, Adv. Stud. Pure Math. 57, 293--302 (2010; Zbl 1210.53041)]. This works extends a number of earlier results. The paper finishes with a number of interesting applications to some Liouville theorems and a two-sided heat kernel bound for Alexandrov spaces.
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Alexandrov space
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infinitesimal Bishop-Gromov condition
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parabolic Harnack inequality
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heat kernel
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harmonic functions
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subharmonic functions
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