Mean value theorems on manifolds

Details Mean value theorems on manifolds Mean value theorems on manifolds

2006-08-24

arxiv.org/abs/math/0608608v1

Mathematics

Differential Geometry

Scientific paper

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.

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