Foliations of 3-manifolds of Positive Scalar Curvature by Surfaces of Controlled Size
Channel: UMD Mathematics
Date: 2021-04-27

Yevgeny Liokumovich (University of Toronto)

Abstract: 
Let M be a compact 3-manifold with scalar curvature at least 1. We show that there exists a Morse function f on M, such that every connected component of every fiber of f has genus, area and diameter bounded by a universal constant. The proof uses Min-Max theory and Mean Curvature Flow. This is a joint work with Davi Maximo. Time permitting, I will discuss a related problem for macroscopic scalar curvature in metric spaces (joint with Boris Lishak, Alexander Nabutovsky and Regina Rotman).