%0 Journal Article
%T Monotonicity theorems for Laplace Beltrami operator on Riemannian manifolds
%A Eduardo V Teixeira
%A Lei Zhang
%J Mathematics
%D 2008
%I arXiv
%X For free boundary problems on Euclidean spaces, the monotonicity formulas of Alt-Caffarelli-Friedman and Caffarelli-Jerison-Kenig are cornerstones for the regularity theory as well as the existence theory. In this article we establish the analogs of these results for the Laplace-Beltrami operator on Riemannian manifolds. As an application we show that our monotonicity theorems can be employed to prove the Lipschitz continuity for the solutions of a general class of two-phase free boundary problems on Riemannian manifolds.
%U http://arxiv.org/abs/0812.0229v3