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ISSN 1079-6762

 

Harmonic functions on Alexandrov spaces and their applications


Author: Anton Petrunin
Translated by:
Journal: Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 135-141
MSC (2000): Primary 51K10; Secondary 31B99
Published electronically: December 17, 2003
MathSciNet review: 2030174
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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.


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Additional Information

Anton Petrunin
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, PA 16802
Email: petrunin@math.psu.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-03-00120-3
PII: S 1079-6762(03)00120-3
Received by editor(s): March 4, 2003
Published electronically: December 17, 2003
Additional Notes: 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.
Communicated by: Dmitri Burago
Article copyright: © Copyright 2003 American Mathematical Society