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Harmonic functions on Alexandrov spaces and their applications
Author(s):
Anton
Petrunin
Journal:
Electron. Res. Announc. Amer. Math. Soc.
9
(2003),
135-141.
MSC (2000):
Primary 51K10;
Secondary 31B99
Posted:
December 17, 2003
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Abstract:
The main result can be stated roughly as follows: Let  be an Alexandrov space,  an open domain and  a harmonic function. Then  is Lipschitz on any compact subset of  . 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:
10.1090/S1079-6762-03-00120-3
PII:
S 1079-6762(03)00120-3
Received by editor(s):
March 4, 2003
Posted:
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
Copyright of article:
Copyright
2003,
American Mathematical Society
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