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

doi:10.2140/pjm.2015.278.173

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 应用数学研究所

	THE W-ENTROPY FORMULA FOR THE WITTEN LAPLACIAN ON MANIFOLDS WITH TIME DEPENDENT METRICS AND POTENTIALS
	Li, Songzi 1,2; Li, Xiang-Dong3
刊名	PACIFIC JOURNAL OF MATHEMATICS
	2015-11-01
卷号	278 期号:1 页码:173-199
ISSN号	0030-8730
DOI	10.2140/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
出版者	PACIFIC JOURNAL MATHEMATICS
WOS记录号	WOS:000362280200007
内容类型	期刊论文
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.