图 书 馆
度量测度空间与合成Ricci界Metric measure spaces and synthetic Ricci bounds |
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| 课程网址: | https://videolectures.net/8ecm2021_theodor_sturm_metric/ |
| 主讲教师: | 信息不详。欢迎您在右侧留言补充。 |
| 开课单位: | 8ECM会议 |
| 开课时间: | 2021-07-06 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Metric measure spaces with synthetic Ricci bounds have attracted great interest in recent years, accompanied by spectacular breakthroughs and deep new insights. In this talk, I will provide a brief introduction to the concept of lower Ricci bounds as introduced by Lott-Villani and myself, and illustrate some of its geometric, analytic and probabilistic consequences, among them Li-Yau estimates, coupling properties for Brownian motions, sharp functional and isoperimetric inequalities, rigidity results, and structural properties like rectifiability and rectifiability of the boundary. In particular, I will explain its crucial interplay with the heat flow and its link to the curvature-dimension condition formulated in functional-analytic terms by Bakry-Emery. This ´ equivalence between the Lagrangian and the Eulerian approach then will be further explored in various recent research directions: i) distribution-valued Ricci bounds which e.g. allow singular effects of non-convex boundaries to be taken into account, ii) time-dependent Ricci bounds which provide a link to (super-) Ricci flows for singular spaces, iii) upper curvature bounds. |
| 关 键 词: | 度量测度空间; 合成Ricci界; 概率结果 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2024-05-28：liyq |
| 最后编审: | 2024-05-28：liyq |
| 阅读次数: | 4 |