Asymptotic estimates on the time derivative of $\Phi$-entropy on Riemannian manifolds

Bin Qian

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arXiv · 1104.3204

Asymptotic estimates on the time derivative of $\Phi$-entropy on Riemannian manifolds

Bin Qian

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Abstract

In this note, we obtain the asymptotic estimate for the time derivative of the $\Phi$-entropy in terms of the lower bound on the Bakry-Emery $\Gamma_2$ curvature. In the cases of Hyperbolic space and Heisenberg group, we show that the time derivative of the $\Phi$-entropy is non-increasing, and we also get sharp asymptotic bound for the time derivative of the entropy in the Heisenberg group.

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Bin Qian. 2011-04-16. Asymptotic estimates on the time derivative of $\Phi$-entropy on Riemannian manifolds. https://arxiv.org/abs/1104.3204

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