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Harmonic functions on Alexandrov spaces and their applications
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## Harmonic functions on Alexandrov spaces and their applications

### Anton Petrunin

**Abstract.**
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.

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