In this talk, which is a continuation of Or Hershkovits’ talk from April 2,  we will describe our resolution of the mean convex neighborhood conjecture for mean curvature flows in R^3. In this second talk of the two, we will discuss about some key techniques of the proof including local L^2 decomposition of the flow. In particular, we will show how to determine dominate eigenfunctions of ancient flows, and will study how to derive geometric properties from given dominate eigenfunctions. We will begin with a short review of Or Hershkovits's talk. 

This is based on a joint work with Robert Haslhofer and Or Hershkovits.