Diff. Geom, Math. Phys., PDE Seminar: Pengfei Guan

  • Date: 10/24/2017
  • Time: 15:30
Pengfei Guan, McGill

University of British Columbia


An isometric embedding problem and related geometric inequalities


Solutions to the classical Weyl problem by Nirenberg and Pogorelov
play fundamental role in the notion of quasi local masses and positive quasi
local mass theorems in general relativity. An interesting question in
differential geometry is whether one can isometrically embed compact surfaces
with positive Gauss curvature to a general 3 dimensional ambient space. Of
particular importance is the anti de Sitter Schwarzchild space in general
relativity. We discuss some recent progress in this direction, the a priori
estimates for embedded surfaces in a joint work with Lu, the openness and
non-rigidity results of Li -Wang, and a new quasi local type inequality of
Lu-Miao. We will also discuss open problem related to isometric embeddings to
ambient spaces with horizons.

Other Information: 

Location: ESB 2012
Tue 24 Oct 2017, 3:30pm-4:30pm