Uniqueness of two-convex closed ancient solutions to the mean curvature flow

Pages 353-436 from Volume 192 (2020), Issue 2 by Sigurd Angenent, Panagiota Daskalopoulos, Natasa Sesum

Abstract

In this paper we consider the classification of closed non-collapsed ancient solutions to the Mean Curvature Flow ($n\geq 2$) that are uniformly two-convex. We prove that they are either contracting spheres or they must coincide up to translations and scaling with the rotationally symmetric closed ancient non-collapsed solution first constructed by Brian White, and later by Robert Haslhofer and Or Hershkovits.

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Keywords
, ,
Mathematical Subject Classification
Primary: ,
DOI
https://doi.org/10.4007/annals.2020.192.2.2
MR
4151080
Milestones
Received: 5 September 2018
Revised: 6 May 2020
Accepted: 12 July 2020
Published online: 9 September 2020

Authors

Sigurd Angenent

University of Wisconsin - Madison, Madison, WI

Panagiota Daskalopoulos

Columbia University, New York, NY

Natasa Sesum

Rutgers University, Piscataway, NJ