Long-time behavior of $3$–dimensional Ricci flow, B: Evolution of the minimal area of simplicial complexes under Ricci flow

Abstract

In this second part of a series of papers on the long-time behavior of Ricci flows with surgery, we establish a bound on the evolution of the infimal area of simplicial complexes inside a $3$–manifold under the Ricci flow. This estimate generalizes an area estimate of Hamilton, which we will recall in the first part of the paper.

We remark that in this paper we will mostly be dealing with nonsingular Ricci flows. The existence of surgeries will not play an important role.