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Asymptotic estimates on the time derivative of entropy on a Riemannian manifold
-
A. P. C. Lim
and
D. Luo
Published/Copyright:
January 8, 2013
Abstract
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.
Published Online: 2013-01-08
Published in Print: 2013-01
© 2013 by Walter de Gruyter GmbH & Co.
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Keywords for this article
Heat equation;
entropy;
Ricci curvature;
Ornstein-Uhlenbeck operator;
hyperbolic space.
Articles in the same Issue
- Masthead
- A class of lattices and boolean functions related to the Manickam–Miklös–Singhi conjecture
- Blocking semiovals containing conics
- On universal covers in normed planes
- Stability results for some classical convexity operations
- Pseudo-embeddings and pseudo-hyperplanes
- Asymptotic estimates on the time derivative of entropy on a Riemannian manifold
- Metrics in the family of star bodies
- Ellipsoid characterization theorems
- Logarithmic limit sets of real semi-algebraic sets
