Volume 22, issue 2 (2018)

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

Richard H Bamler

Geometry & Topology 22 (2018) 845–892
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.

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Keywords
Ricci flow, minimal surfaces, minimal surfaces with junctions, minimal simplicial complexes, boundary regularity
Mathematical Subject Classification 2010
Primary: 49Q05, 53C44
Secondary: 57M20
Publication
Received: 16 December 2014
Revised: 22 July 2015
Accepted: 21 January 2017
Published: 16 January 2018
Proposed: Tobias H. Colding
Seconded: Bruce Kleiner, Gang Tian
Authors
 Richard H Bamler Department of Mathematics University of California Berkeley, CA United States https://math.berkeley.edu/~rbamler/