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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
Source PublicationPACIFIC JOURNAL OF MATHEMATICS
ISSN0030-8730
Volume278Issue:1Pages:173-199
AbstractWe 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.
DOI10.2140/pjm.2015.278.173
Language英语
Funding ProjectChina Scholarship Council ; NSFC[11371351] ; Key Laboratory of Random Complex Structures and Data Science, AMSS, CAS[2008DP173182] ; Hundred Talents Project of AMSS, CAS
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000362280200007
PublisherPACIFIC JOURNAL MATHEMATICS
Citation statistics
Cited Times:8[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20868
Collection应用数学研究所
Affiliation1.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
Recommended Citation
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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