Abstract:

We report our recent work on a classical problem in geometric analysis: isometric immersions and/or embeddings of Riemannian and semi-Riemannian manifolds. The underlying PDE (partial differential equation) is the Gauss-Codazzi-Ricci equations. Existence of isometric immersions is studied under various curvature conditions, via elliptic and hyperbolic PDE techniques. Weak continuity of isometric immersions is investigated with the help of the theory of compensated compactness. Connections to other problems, including harmonic maps and Coloumb gauges, will also be discussed.

Our talk contains joint works with Gui-Qiang Chen and Marshall Slemrod.

Speaker：

Siran Li

2017年从英国牛津大学获得博士学位，师从陈贵强教授。2017-2019年在美国莱斯大学进行博士后研究，导师为Robert Hardt教授。2020-2021年在上海纽约大学任访问助理教授。2021年9月起任上海交通大学副教授。主要从事偏微分方程方向的研究，特别关注来源于流体力学及微分几何问题的微分方程。目前已在国际国内知名期刊上发表论文二十余篇。

Siran Li: School of Mathematical Sciences, Shanghai Jiao Tong University, No. 6 Science Buildings, 800 Dongchuan Road, Minhang District, Shanghai, China (200240)
Siran Li: Key Laboratory of Scientific and Engineering Computing (Ministry of Education), Shanghai Jiao Tong University, No. 6 Science Buildings, 800 Dongchuan Road, Minhang District, Shanghai, China (200240)
Siran Li: New York University - Shanghai, Office 1146, 1555 Century Avenue, Pudong District, Shanghai, China (200122)
Siran Li: NYU-ECNU Institute of Mathematical Sciences, Room 340, Geography Building, 3663 North Zhongshan Road, Shanghai, China (200062)

Zoom:

https://us02web.zoom.us/j/82156646127?pwd=N1JSOStwcmV1dUdHanNSWkwzRGlhQT09

Passwords: 529643