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THE W-ENTROPY FORMULA FOR THE WITTEN LAPLACIAN ON MANIFOLDS WITH TIME DEPENDENT METRICS AND POTENTIALS

文献类型：期刊论文

作者Li, Songzi1,2; Li, Xiang-Dong3
刊名PACIFIC JOURNAL OF MATHEMATICS
出版日期2015-11-01
卷号278期号:1页码:173-199
ISSN号0030-8730
DOI10.2140/pjm.2015.278.173
英文摘要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.
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
语种英语
WOS记录号WOS:000362280200007
出版者PACIFIC JOURNAL MATHEMATICS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/20867]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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