W-Entropy, Super Perelman Ricci Flows, and (K, m)-Ricci Solitons

doi:10.1007/s12220-019-00193-4

CSpace > 应用数学研究所

	W-Entropy, Super Perelman Ricci Flows, and (K, m)-Ricci Solitons
	Li, Songzi 1; Li, Xiang-Dong2,3
	2020-07-01
发表期刊	JOURNAL OF GEOMETRIC ANALYSIS
ISSN	1050-6926
卷号	30 期号:3 页码:3149-3180
摘要	In this paper, we prove a characterization of (K, infinity)-super Perelman Ricci flows by functional inequalities and gradient estimate for the heat semigroup generated by the Witten Laplacian on manifolds equipped with time-dependent metrics and potentials. As a byproduct, we derive the Hamilton type dimension-free Harnack inequality on manifolds with (K, infinity)-super Perelman Ricci flows. Based on a new entropy differential inequality for the heat equation of the Witten Laplacian, we introduce a new W-entropy quantity and prove its monotonicity for the heat equation of the Witten Laplacian On complete Riemannian manifolds with the C D(K, infinity)-condition and on compact manifolds with (K, infinity)-super Perelman Ricci flows. Our results characterize the (K, infinity)-Ricci solitons and the (K, infinity)-Perelman Ricci flows. We also prove an entropy differential inequality on (K, m)-super Perelman Ricci flows, which can be used to characterize the (K, m)-Ricci solitons and the (K, m)-Perelman Ricci flows. Finally, we show that the Gaussian-type solitons on R-m provide asymptotical rigidity models for the W-m,W-K-entropy on manifolds with the CD(-K, m)-condition.
关键词	W-entropy Witten Laplacian CD(K, m)-condition (K, m)-Ricci solitons (K, m)-super Perelman Ricci flows (K, m)-Perelman Ricci flow Gaussian solitons
DOI	10.1007/s12220-019-00193-4
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000556209700033
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51935
专题	应用数学研究所
通讯作者	Li, Xiang-Dong
作者单位	1.Renmin Univ China, Sch Math, 59 Zhongguancun Da Jie, Beijing 100872, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, 55 Zhongguancun East Rd, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Li, Songzi,Li, Xiang-Dong. W-Entropy, Super Perelman Ricci Flows, and (K, m)-Ricci Solitons[J]. JOURNAL OF GEOMETRIC ANALYSIS,2020,30(3):3149-3180.
APA	Li, Songzi,&Li, Xiang-Dong.(2020).W-Entropy, Super Perelman Ricci Flows, and (K, m)-Ricci Solitons.JOURNAL OF GEOMETRIC ANALYSIS,30(3),3149-3180.
MLA	Li, Songzi,et al."W-Entropy, Super Perelman Ricci Flows, and (K, m)-Ricci Solitons".JOURNAL OF GEOMETRIC ANALYSIS 30.3(2020):3149-3180.