Harmonic functions on alexandrov spaces and their applications

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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 languageEnglish (US)
Pages (from-to)135-141
Number of pages7
JournalElectronic Research Announcements of the American Mathematical Society
Volume9
Issue number17
DOIs
StatePublished - Dec 17 2003

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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