In this talk, which will be supplemented by the talk of Kyeongsu Choi on April 12th,  we will describe our resolution of the mean convex neighborhood conjecture for mean curvature flows in R^3.

In this first talk of the two, which will assume no prior familiarity with mean curvature flow,  I will describe the relevant background needed to state the mean convex neighborhood conjecture, and explain how this conjecture follows from a classification result of   ancient low entropy (singular) mean curvature flows. I will also describe the relation between the conjecture and uniqueness. Time permitting, I will outline the major steps in the proof.

More detailed account of the proof will then be given in Kyeongsu Choi’s talk on April 12th. 

This is based on a joint work with Kyeongsu Choi and Robert Haslhofer.