Differential Geometry Working SeminarExport this event to calendar

Thursday, January 27, 2022 — 1:00 PM EST

Daren Cheng, Department of Pure Mathematics, University of Waterloo

"Incompressible minimal surfaces and topological consequences of positive scalar curvature (Part 3)"

I will continue talking about the paper by Schoen and Yau (Annals, 1979) on the topological consequences of positive scalar curvature on 3-manifolds, focusing on the following special case of their main theorem: a closed 3-manifold admits no positive scalar curvature (PSC) metric if its fundamental group contains a subgroup isomorphic to Z \oplus Z. I will begin with a quick review of my two previous talks, in which I explained how the PSC condition forbids the existence of immersed stable minimal tori, outlined how to use the assumption on the fundamental group to construct such a minimal torus, and described the initial steps of this latter construction. I will then attempt to explain the remainder of the construction, which involves minimizing the Dirichlet energy in two stages. Some classical regularity and compactness results for energy-minimizing harmonic maps will be taken for granted.

Zoom link: https://uwaterloo.zoom.us/j/95873618652?pwd=OENSeFdERzUzV2NkM3hjQ0F1MzFYUT09

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