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