By Anthony Genevois
By Otis Chodosh
By Michael Eichmair
By Daniel Stern
Appears in collection : Not Only Scalar Curvature Seminar
We'll discuss a circle of ideas developed over the last few years relating scalar curvature lower bounds to the structure of level sets of solutions to certain geometric pdes on 3-manifolds. We'll describe applications to the study of 3-manifold geometry and initial data sets in general relativity, drawing comparisons with other pde methods for detecting the influence of scalar curvature.