Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions

Brendle, Simon; Choi, Kyeongsu

doi:10.2140/gt.2021.25.2195

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Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions

Simon Brendle and Kyeongsu Choi

Geometry & Topology 25 (2021) 2195–2234

DOI: 10.2140/gt.2021.25.2195

Abstract

We consider noncompact ancient solutions to the mean curvature flow in $ℝ^{n + 1}$ ( $n \geq 3$ ) which are strictly convex, uniformly two-convex, and noncollapsed. We prove that such an ancient solution is a rotationally symmetric translating soliton.

Keywords

mean curvature flow, ancient solution

Mathematical Subject Classification 2010

Primary: 53C44

References

Publication

Received: 16 December 2018

Revised: 11 February 2020

Accepted: 17 July 2020

Published: 3 September 2021

Proposed: Bruce Kleiner

Seconded: John Lott, Tobias H Colding

Authors

Simon Brendle
Department of Mathematics Columbia University New York, NY United States

Kyeongsu Choi
School of Mathematics Korea Institute for Advanced Study Seoul South Korea

Volume 25, issue 5 (2021)