Asymptotic estimates on the time derivative of entropy on a Riemannian manifold

Details Asymptotic estimates on the time derivative of entropy on a Riemannian manifold Asymptotic estimates on the time derivative of entropy on a Riemannian manifold

2010-11-17

arxiv.org/abs/1011.3979v2

Mathematics

Differential Geometry

15 pages

Scientific paper

We consider the entropy of the solution to the heat equation on a Riemannian manifold. When the manifold is compact, we provide two estimates on the rate of change of the entropy in terms of the lower bound on the Ricci curvature and the spectral gap respectively. Our explicit computation for the three dimensional hyperbolic space shows that the time derivative of the entropy is asymptotically bounded by two positive constants.

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