A characterization of the rate of change of Phi-entropy via an integral form curvature-dimension condition
文献类型：期刊论文
| 作者 | Luo, Dejun
|
| 刊名 | ADVANCES IN GEOMETRY
 |
| 出版日期 | 2016-07-01 |
| 卷号 | 16期号:3页码:277-290 |
| 关键词 | Heat equation Phi-entropy curvature-dimension condition second fundamental form reflecting diffusion semigroup |
| ISSN号 | 1615-715X |
| DOI | 10.1515/advgeom-2015-0046 |
| 英文摘要 | Let M be a compact Riemannian manifold without boundary and V : M -> R a smooth function. Denote by P-t and d mu = e(V) dx the semigroup and symmetric measure of the second order differential operator L = Delta + del V center dot del. For some suitable convex function Phi : J -> R defined on an interval I, we consider the Phi-entropy of P(t)f (with respect to mu) for any f is an element of C-infinity (M, J). We show that an integral form curvature-dimension condition is equivalent to an estimate on the rate of change of the Phi-entropy. We also generalize this result to bounded smooth domains of a complete Riemannian manifold. |
| 语种 | 英语 |
| WOS记录号 | WOS:000381015500002 |
| 出版者 | WALTER DE GRUYTER GMBH |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/23306]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Luo, Dejun |
| 作者单位 | Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Luo, Dejun. A characterization of the rate of change of Phi-entropy via an integral form curvature-dimension condition[J]. ADVANCES IN GEOMETRY,2016,16(3):277-290. |
| APA | Luo, Dejun.(2016).A characterization of the rate of change of Phi-entropy via an integral form curvature-dimension condition.ADVANCES IN GEOMETRY,16(3),277-290. |
| MLA | Luo, Dejun."A characterization of the rate of change of Phi-entropy via an integral form curvature-dimension condition".ADVANCES IN GEOMETRY 16.3(2016):277-290. |
入库方式： OAI收割
来源：数学与系统科学研究院
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