A characterization of the rate of change of Phi-entropy via an integral form curvature-dimension condition

doi:10.1515/advgeom-2015-0046

CSpace > 应用数学研究所

	A characterization of the rate of change of Phi-entropy via an integral form curvature-dimension condition
	Luo, Dejun
	2016-07-01
发表期刊	ADVANCES IN GEOMETRY
ISSN	1615-715X
卷号	16 期号:3 页码:277-290
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.
关键词	Heat equation Phi-entropy curvature-dimension condition second fundamental form reflecting diffusion semigroup
DOI	10.1515/advgeom-2015-0046
语种	英语
资助项目	Key Laboratory of Random Complex Structures and Data Sciences, Chinese Academy of Sciences[2008DP173182] ; Natural Science Foundation of China[11371099] ; Academy of Mathematics and Systems Science[Y129161ZZ1]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000381015500002
出版者	WALTER DE GRUYTER GMBH
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23307
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.