Harmonic functions on Alexandrov spaces and their applications

Abstract

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