Volume 25, issue 5 (2021)

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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
Abstract

We consider noncompact ancient solutions to the mean curvature flow in n+1 (n 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