W-Entropy, Super Perelman Ricci Flows, and (K, m)-Ricci Solitons
文献类型：期刊论文
| 作者 | Li, Songzi3; Li, Xiang-Dong1,2
|
| 刊名 | JOURNAL OF GEOMETRIC ANALYSIS
 |
| 出版日期 | 2020-07-01 |
| 卷号 | 30期号:3页码:3149-3180 |
| 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 |
| ISSN号 | 1050-6926 |
| DOI | 10.1007/s12220-019-00193-4 |
| 英文摘要 | 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. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000556209700033 |
| 出版者 | SPRINGER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51934]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Li, Xiang-Dong |
| 作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, 55 Zhongguancun East Rd, Beijing 100190, Peoples R China 3.Renmin Univ China, Sch Math, 59 Zhongguancun Da Jie, Beijing 100872, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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