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Learning Seminar on PDE and Applications

Generalized soap bubbles and the topology of manifolds with positive scalar curvature

Chao, Li, Princeton University

Location:  https://rutgers.zoom.us/j/94841604914?pwd=TXZzV0hjVWdZcTYxRGErYTFoeWNLZz09
Date & time: Friday, 20 November 2020 at 2:00PM - 4:00PM

Abstract: It has been a classical question which  manifolds admit Riemannian metrics with positive scalar curvature. I will first review some history of this question, and present some recent progress, ruling out positive scalar curvature on closed aspherical manifolds of dimensions 4 and 5 (as conjectured by Schoen-Yau and by Gromov), as well as complete metrics of positive scalar curvature on an arbitrary manifold connect sum with a torus.  Applications include Schoen-Yau Liouville theorem for all locally conformally flat manifolds. The proofs of these results are based on analyzing generalized soap bubbles - surfaces that are stable solutions to the prescribed mean curvature problem.  This talk is based on joint work with O. Chodosh.

Meeting ID 948 4160 4914
Passcode: 654986

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