Harmonic functions on Alexandrov spaces and their applications

Petrunin, Anton¹

¹ Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 135-141

Résumé

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.

Détail

DOI : 10.1090/S1079-6762-03-00120-3

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