Mean value theorems on manifolds
Differential Geometry
2007-05-23 v1
Abstract
We derive several mean value formulae on manifolds, generalizing the classical one for harmonic functions on Euclidean spaces as well as later results of Schoen-Yau, Michael-Simon, etc, on curved Riemannian manifolds. For the heat equation a mean value theorem with respect to `heat spheres' is proved for heat equation with respect to evolving Riemannian metrics via a space-time consideration. Some new monotonicity formulae are derived. As applications of the new local monotonicity formulae, some local regularity theorems concerning Ricci flow are proved.
Cite
@article{arxiv.math/0608608,
title = {Mean value theorems on manifolds},
author = {Lei Ni},
journal= {arXiv preprint arXiv:math/0608608},
year = {2007}
}