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

Copyright 2003 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 09 (2003), pp. 135-141
• Publisher Identifier: S 1079-6762(03)00120-3
• 2000 Mathematics Subject Classification. Primary 51K10; Secondary 31B99
• Received by editors March 4, 2003
• Posted on December 17, 2003
• Communicated by Dmitri Burago
• Comments (When Available)

Anton Petrunin

Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

E-mail address: petrunin@math.psu.edu

The main part of this paper was written while I had postdoctoral fellowship at MSRI in 1995--1996. I would like to thank this institute for providing excellent conditions to conduct this research. I was also supported by NSF DMS-0103957.