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學術演講

Analysis Seminar

Partial Differential Equations of mixed types and the problem of isometric immersions

2025/04/08 (Tue.) 10:00~13:00
  • 日期 : 2025/04/08 (Tue.) 10:00~13:00
  • 地點 : online
  • 主講人 : Siran Li (Shanghai Jiao Tong University)
  • 籌辦人 : Tai-Ping Liu (AS)
  • 演講摘要 : 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 Sobolev 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 continuity of Gauss--Codazzi--Ricci equations, the weak stability of isometric immersions, and the fundamental theorem of submanifold theory with low regularity. Two mixed-type PDE techniques are emphasised throughout these developments: the method of compensated compactness and the theory of Coulomb--Uhlenbeck gauges.

【Registration】
Online participants must fill the application form below. A link to the meeting will be distributed on a first-come, first-serve basis, due to device limitations.
Click here to register (Deadline: 4PM, Apr. 7)

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