Asymptotic estimates on the time derivative of \(\Phi\)-entropy on Riemannian manifolds (Q2452407)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic estimates on the time derivative of \(\Phi\)-entropy on Riemannian manifolds |
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Asymptotic estimates on the time derivative of \(\Phi\)-entropy on Riemannian manifolds (English)
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3 June 2014
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The author derives bounds for the time derivative of the \(\Phi\)-entropy of the solution of the heat equation on a Riemannian manifold, under a curvature-dimension condition on the carre du champ operator associated to the Laplacian. Concavity in time and sharp asymptotic bounds for the time derivative of the \(\Phi\)-entropy are deduced, notably on hyperbolic spaces and for the Heisenberg group.
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\(\Phi\)-entropy
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curvature
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heat kernel
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hyperbolic space
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0.9709926
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0.8724234
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0.8670551
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0.86569625
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0.8645079
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0.8630966
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