Asymptotic estimates on the time derivative of $\Phi$-entropy on Riemannian manifolds
Differential Geometry
2011-08-12 v2
Abstract
In this note, we obtain the asymptotic estimate for the time derivative of the -entropy in terms of the lower bound on the Bakry-Emery curvature. In the cases of Hyperbolic space and Heisenberg group, we show that the time derivative of the -entropy is non-increasing, and we also get sharp asymptotic bound for the time derivative of the entropy in the Heisenberg group.
Keywords
Cite
@article{arxiv.1104.3204,
title = {Asymptotic estimates on the time derivative of $\Phi$-entropy on Riemannian manifolds},
author = {Bin Qian},
journal= {arXiv preprint arXiv:1104.3204},
year = {2011}
}
Comments
This paper has been withdrawn by the author since we will modify it deeply