Mean value theorems on manifolds

Lei Ni

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arXiv · math/0608608

Mean value theorems on manifolds

Lei Ni

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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.

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Lei Ni. 2006-08-24. Mean value theorems on manifolds. https://arxiv.org/abs/math/0608608

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