Open Access
June 2007 Mean Value Theorems on Manifolds
Lei Ni
Asian J. Math. 11(2): 277-304 (June 2007).


We derive several mean value formulae on manifolds, generalizing the classical one for harmonic functions on Euclidean spaces as well as the 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 spacetime 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. "Mean Value Theorems on Manifolds." Asian J. Math. 11 (2) 277 - 304, June 2007.


Published: June 2007
First available in Project Euclid: 31 July 2007

zbMATH: 1139.58018
MathSciNet: MR2328895

Primary: 58J35

Keywords: Green’s function , heat spheres/balls , local regularity theorem , mean value theorem , Ricci flow

Rights: Copyright © 2007 International Press of Boston

Vol.11 • No. 2 • June 2007
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