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Uniqueness of convex ancient solutions to mean curvature flow in \({\mathbb {R}}^3\)

  • Simon BrendleEmail author
  • Kyeongsu Choi
Article
  • 110 Downloads

Abstract

A well-known question of Perelman concerns the classification of noncompact ancient solutions to the Ricci flow in dimension 3 which have positive sectional curvature and are \(\kappa \)-noncollapsed. In this paper, we solve the analogous problem for mean curvature flow in \({\mathbb {R}}^3\), and prove that the rotationally symmetric bowl soliton is the only noncompact ancient solution of mean curvature flow in \({\mathbb {R}}^3\) which is strictly convex and noncollapsed.

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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