Asian Journal of Mathematics
- Asian J. Math.
- Volume 11, Number 2 (2007), 277-304.
Mean Value Theorems on Manifolds
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.
Asian J. Math., Volume 11, Number 2 (2007), 277-304.
First available in Project Euclid: 31 July 2007
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 58J35: Heat and other parabolic equation methods
Ni, Lei. Mean Value Theorems on Manifolds. Asian J. Math. 11 (2007), no. 2, 277--304. https://projecteuclid.org/euclid.ajm/1185891805