Differential Geometry Working Seminar

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:

• Zoom link: https://uwaterloo.zoom.us/j/95873618652?pwd=OENSeFdERzUzV2NkM3hjQ0F1MzFYUT09
• Room: MC 5403