Harmonic functions on alexandrov spaces and their applications

Anton Petrunin

doi:10.1090/S1079-6762-03-00120-3

Harmonic functions on alexandrov spaces and their applications

Anton Petrunin

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

The main result can be stated roughly as follows: Let M be an Alexandrov space, Ω ⊂ M an open domain and f: Ω → ℝ a harmonic function. Then f is Lipschitz on any compact subset of. Ω Using this result I extend proofs of some classical theorems in Riemannian geometry to Alexandrov spaces.

Original language	English (US)
Pages (from-to)	135-141
Number of pages	7
Journal	Electronic Research Announcements of the American Mathematical Society
Volume	9
Issue number	17
DOIs	https://doi.org/10.1090/S1079-6762-03-00120-3
State	Published - Dec 17 2003

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1090/S1079-6762-03-00120-3

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AB - The main result can be stated roughly as follows: Let M be an Alexandrov space, Ω ⊂ M an open domain and f: Ω → ℝ a harmonic function. Then f is Lipschitz on any compact subset of. Ω Using this result I extend proofs of some classical theorems in Riemannian geometry to Alexandrov spaces.

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U2 - 10.1090/S1079-6762-03-00120-3

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Harmonic functions on alexandrov spaces and their applications

Abstract

All Science Journal Classification (ASJC) codes

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