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

Bamler, Richard

doi:10.2140/gt.2018.22.845

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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

DOI: 10.2140/gt.2018.22.845

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.

Keywords

Ricci flow, minimal surfaces, minimal surfaces with junctions, minimal simplicial complexes, boundary regularity

Mathematical Subject Classification 2010

Primary: 49Q05, 53C44

Secondary: 57M20

References

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/

Volume 22, issue 2 (2018)