Analysis & Applied Math

Event Information The Weyl isometric embedding problem to general 3D Riemannian manifolds
13:10 on Friday March 03, 2017
14:00 on Friday March 03, 2017
FI230, Fields Institute, 222 College St.
Pengfei Guan

McGill University

The classical Weyl problem asks isometric embedding of positively curved compact surface in to R^3, which was solved by Nirenberg in 1950s. Pogorelov subsequently solved the Weyl problem in hyperbolic space H^3, he also considered the problem in general 3D Riemannian manifolds. Solutions to Weyl's problem in R^3 and H^3 have important applications in general relativity, e.g. the Brown-York, Liu-Yau and Wang-Yau quasi local masses. We report some recent progress on the Weyl problem of isometric embeddings of (S^2, g) to general 3D ambient space: the openness and non-rigidity results C. Li and Z. Wang, the curvature estimates for immersed surfaces jointly with Siyuan Lu, and the existence of solutions of the problem when the surface contains no horizon. We will also discuss the problem when horizon arises.

The Analysis & Applied Math Seminar this week is joint with the Fields Geometric Analysis Colloquium, see http://www.fields.utoronto.ca/activities/seminars/geometric-analysis-colloquium-0