KMS Of Academy of mathematics and systems sciences, CAS
THE W-ENTROPY FORMULA FOR THE WITTEN LAPLACIAN ON MANIFOLDS WITH TIME DEPENDENT METRICS AND POTENTIALS | |
Li, Songzi1,2; Li, Xiang-Dong3 | |
2015-11-01 | |
发表期刊 | PACIFIC JOURNAL OF MATHEMATICS |
ISSN | 0030-8730 |
卷号 | 278期号:1页码:173-199 |
摘要 | We develop a new approach to prove the W-entropy formula for the Witten Laplacian via warped product on Riemannian manifolds, giving a natural geometric interpretation of the quantities appearing in the W-entropy formula. We also prove the W-entropy formula for the Witten Laplacian on compact Riemannian manifolds with time dependent metrics and potentials, as well as for the backward heat equation associated with the Witten Laplacian on compact Riemannian manifolds equipped with Lott's modified Ricci flow. Our results extend to complete Riemannian manifolds with negative m-dimensional Bakry Emery Ricci curvature, and to compact Riemannian manifolds with K-super m-dimensional Bakry Emery Ricci flow. As an application, we prove that the optimal logarithmic Sobolev constant on compact manifolds equipped with the K-super m-dimensional Bakry Emery Ricci flow is decreasing in time. |
DOI | 10.2140/pjm.2015.278.173 |
语种 | 英语 |
资助项目 | China Scholarship Council ; NSFC[11371351] ; Key Laboratory of Random Complex Structures and Data Science, AMSS, CAS[2008DP173182] ; Hundred Talents Project of AMSS, CAS |
WOS研究方向 | Mathematics |
WOS类目 | Mathematics |
WOS记录号 | WOS:000362280200007 |
出版者 | PACIFIC JOURNAL MATHEMATICS |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/20868 |
专题 | 应用数学研究所 |
通讯作者 | Li, Songzi |
作者单位 | 1.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China 2.Univ Toulouse 3, Inst Math Toulouse, F-31062 Toulouse 9, France 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
推荐引用方式 GB/T 7714 | Li, Songzi,Li, Xiang-Dong. THE W-ENTROPY FORMULA FOR THE WITTEN LAPLACIAN ON MANIFOLDS WITH TIME DEPENDENT METRICS AND POTENTIALS[J]. PACIFIC JOURNAL OF MATHEMATICS,2015,278(1):173-199. |
APA | Li, Songzi,&Li, Xiang-Dong.(2015).THE W-ENTROPY FORMULA FOR THE WITTEN LAPLACIAN ON MANIFOLDS WITH TIME DEPENDENT METRICS AND POTENTIALS.PACIFIC JOURNAL OF MATHEMATICS,278(1),173-199. |
MLA | Li, Songzi,et al."THE W-ENTROPY FORMULA FOR THE WITTEN LAPLACIAN ON MANIFOLDS WITH TIME DEPENDENT METRICS AND POTENTIALS".PACIFIC JOURNAL OF MATHEMATICS 278.1(2015):173-199. |
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