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

TL;DR

This paper investigates how the minimal area of simplicial complexes in a 3-manifold evolves under Ricci flow, providing bounds that extend Hamilton's earlier estimates, mainly focusing on non-singular flows.

Contribution

It establishes a new bound on the evolution of the infimal area of simplicial complexes during Ricci flow, generalizing previous results by Hamilton.

Findings

Derived bounds on minimal area evolution under Ricci flow

Extended Hamilton's area estimate to broader settings

Focused on non-singular Ricci flows without surgeries

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 non-singular Ricci flows. The existence of surgeries will not play an important role.