Mathematics – Differential Geometry
Scientific paper
2009-11-10
Mathematics
Differential Geometry
Scientific paper
The purpose of this work is to study some monotone functionals of the heat kernel on a complete Riemannian manifold with nonnegative Ricci curvature. In particular, we show that on these manifolds, the gradient estimate of Li and Yau, the gradient estimate of Ni, the monotonicity of the Perelman's entropy and the volume doubling property are all consequences of an entropy inequality recently discovered by Baudoin-Garofalo. The latter is a linearized version of a logarithmic Sobolev inequality that is due to D. Bakry and M. Ledoux.
Baudoin Fabrice
Garofalo Nicola
No associations
LandOfFree
Perelman's entropy and doubling property on Riemannian manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Perelman's entropy and doubling property on Riemannian manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Perelman's entropy and doubling property on Riemannian manifolds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-50899