Isometric Immersions of Riemannian Manifolds into Euclidean Spaces, Revisited

Abstract: The existence of isometric immersions of Riemannian manifolds into ambient Euclidean spaces has been a classical problem in geometric analysis and nonlinear PDEs. Seminal works by Darboux, Weyl, Nirenberg, Nash, Gromov, etc. etc. have addressed this problem from different perspectives. In this talk we discuss three approaches, some are probably less known, to the isometric immersions problem. These include (1), pseudo-holomorphic curve formulation of the Weyl problem due to F. Labourie; (2), Uhlenbeck gauge formulation for the Pfaff system; and (3), the fluid mechanical formulation for negatively curved surfaces.

Mathematics

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php