题目: Regularity of Lagrangian flows on RCD(K,N) spaces and applications

报告人：Qin Deng（MIT）

时间：2022年10月25日（周二） 09:00-10:00 

会议地点： Zoom 会议

https://us06web.zoom.us/j/88377358987?pwd=L25NT3VSNlRzTndoY0FSbHZpNkNJQT09

Zoom 会议号：883 7735 8987 密码：1958

摘要: In this talk I will discuss regularity results for Regular Lagrangian Flows (RLFs) on RCD(K,N) spaces. RCD(K,N) spaces are metric measure spaces with Ricci curvature bounded below by K and dimension bounded above by N, and captures the well-studied classes of Ricci limit spaces and Alexandrov spaces. RLFs are generalizations of flows via vector field to the nonsmooth setting and an understanding of their spatial regularity has applications in generalizing results from the Riemannian setting where smooth flows are used. Regularity results of this type have been to show the Hölder continuity of tangent cones and non-branching in the RCD setting. Time permitting, I will also discuss some other potential applications in studying the structure and topology of RCD spaces.