Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces

doi:10.1007/s00229-019-01177-y

CSpace > 应用数学研究所

	Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces
	Kuwada, Kazumasa 1; Li, Xiang-Dong2
	2020-01-25
发表期刊	MANUSCRIPTA MATHEMATICA
ISSN	0025-2611
页码	31
摘要	By means of a space-time Wasserstein control, we show the monotonicity of the W-entropy functional in time along heat flows on possibly singular metric measure spaces with non-negative Ricci curvature and a finite upper bound of dimension in an appropriate sense.The associated rigidity result on the rate of dissipation of the W-entropy is also proved.These extend known results even on weighted Riemannian manifolds in some respects. In addition, we reveal that some singular spaces will exhibit the rigidity models while only the Euclidean space does in the class of smooth weighted Riemannian manifolds.
DOI	10.1007/s00229-019-01177-y
收录类别	SCI
语种	英语
资助项目	European Union through the ERC-AdG Ricci Bounds
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000509130500001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50546
专题	应用数学研究所
通讯作者	Kuwada, Kazumasa
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, 55 Zhongguancun East Rd, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Kuwada, Kazumasa,Li, Xiang-Dong. Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces[J]. MANUSCRIPTA MATHEMATICA,2020:31.
APA	Kuwada, Kazumasa,&Li, Xiang-Dong.(2020).Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces.MANUSCRIPTA MATHEMATICA,31.
MLA	Kuwada, Kazumasa,et al."Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces".MANUSCRIPTA MATHEMATICA (2020):31.