Generalized Transportation-Cost Inequalities and Applications |
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Authors: | Feng-Yu Wang |
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Institution: | (1) School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China;(2) Present address: Department of Mathematics, Swansea University, Singleton Park, SA2 8PP Swansea, UK |
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Abstract: | For μ: = e
V(x)dx a probability measure on a complete connected Riemannian manifold, we establish a correspondence between the Entropy-Information
inequality and the transportation-cost inequality for μ(f
2) = 1, where Φ and Ψ are increasing functions. Moreover, under the curvature–dimension condition, a Sobolev type HWI (entropy-cost-information)
inequality is established. As applications, explicit estimates are obtained for the Sobolev constant and the diameter of a
compact manifold, which either extend or improve some corresponding known results.
Supported in part by NNSFC(10721091) and the 973-project in China. |
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Keywords: | Transportation-cost inequality HWI inequality Log-Sobolev inequality Riemannian manifold |
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