Local monotonicity and mean value formulas for evolving Riemannian manifolds
Differential Geometry
2007-05-23 v1 Analysis of PDEs
Abstract
We derive identities for general flows of Riemannian metrics that may be regarded as local mean-value, monotonicity, or Lyapunov formulae. These generalize previous work of the first author for mean curvature flow and other nonlinear diffusions. Our results apply in particular to Ricci flow, where they yield a local monotone quantity directly analogous to Perelman's reduced volume V and a local identity related to Perelman's average energy F.
Keywords
Cite
@article{arxiv.math/0608470,
title = {Local monotonicity and mean value formulas for evolving Riemannian manifolds},
author = {Klaus Ecker and Dan Knopf and Lei Ni and Peter Topping},
journal= {arXiv preprint arXiv:math/0608470},
year = {2007}
}