Asian Journal of Mathematics

Mean Value Theorems on Manifolds

Lei Ni

Full-text: Open access

Abstract

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.

Article information

Source
Asian J. Math., Volume 11, Number 2 (2007), 277-304.

Dates
First available in Project Euclid: 31 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1185891805

Mathematical Reviews number (MathSciNet)
MR2328895

Zentralblatt MATH identifier
1139.58018

Subjects
Primary: 58J35: Heat and other parabolic equation methods

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

Citation

Ni, Lei. Mean Value Theorems on Manifolds. Asian J. Math. 11 (2007), no. 2, 277--304. https://projecteuclid.org/euclid.ajm/1185891805


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