Sharp entropy bounds of closed surfaces and min-max theory

geometric analysis
min-max theory
closed surfaces
sharp entropy

Appears in collection : Summer School 2016 - Geometric Analysis, Metric Geometry and Topology

In 2012, Colding-Ilmanen-Minicozzi-White conjectured that the entropy of any closed surface in R^3 is at least that of the self-shrinking two-sphere. I will explain joint work with X. Zhou where we interpret this conjecture as a parabolic version of the Willmore problem and give a min-max proof of (most cases) of their conjecture.