Foliations of 3-manifolds of positive scalar curvature by surfaces of controlled size (Joint seminar with UCSD)

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. This is a joint work with Davi Maximo.