Differential Geometry Working SeminarExport this event to calendar

Wednesday, November 17, 2021 — 2:30 PM EST

Daren Cheng, Department of Pure Mathematics, University of Waterloo

"Incompressible minimal surfaces and topological consequences of positive scalar curvature (Part 2)"

I'll continue talking about the paper by Schoen-Yau (Annals, '79) on the topology of 3-manifolds admitting positive scalar curvature (PSC) metrics. In Part 1 I explained how the PSC condition is incompatible with the existence of immersed stable minimal tori. In this talk, I'll explain how to produce such a minimal torus when the fundamental group of the 3-manifold contains a copy of Z \oplus Z. The idea is to first construct a \pi_1-injective map from the torus into the 3-manifold, and then find a stable minimal immersion by minimizing the Dirichlet energy first among maps inducing the same \pi_1-action, and then among conformal classes of metrics on the torus.

This seminar will be held jointly online and in person:

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