Speaker: 李思然副教授, 上海交通大学

Inviter: 黄飞敏研究员

Title: Gauss-Codazzi-Ricci equations and the fundamental theorem of submanifold theory of slightly supercritical regularity

Language: Chinese

Time & Venue: 2025.05.08 10:00-11:00 南楼613

Abstract: This talk is about a classical problem in differential geometry and global analysis: the isometric immersions of Riemannian manifolds into Euclidean spaces. We focus on the PDE approach to isometric immersions, i.e., the analysis of Gauss--Codazzi--Ricci equations, especially in the regime of low regularity. Such equations are not purely elliptic, parabolic, or hyperbolic in general, hence calling for analytical tools for PDEs of mixed types. We discuss various recent contributions -- in line with the pioneering works by G.-Q. Chen, M. Slemrod, and D. Wang [Proc. Amer. Math. Soc. (2010); Comm. Math. Phys. (2010)] -- on the weak stability of isometric immersions and the fundamental theorem of submanifold theory with low regularity. Two mixed-type PDE techniques are emphasised: the method of compensated compactness and the theory of Uhlenbeck gauges. （Joint work with Xiangxiang Su.）