# Uniqueness of convex ancient solutions to mean curvature flow in $${\mathbb {R}}^3$$R3

@article{Brendle2019UniquenessOC,
title={Uniqueness of convex ancient solutions to mean curvature flow in \$\$\{\mathbb \{R\}\}^3\$\$R3},
author={Simon Brendle and Kyeongsu Choi},
journal={Inventiones mathematicae},
year={2019},
volume={217},
pages={35-76}
}
• Published 2 November 2017
• Mathematics
• Inventiones mathematicae
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 $$\kappa$$κ-noncollapsed. In this paper, we solve the analogous problem for mean curvature flow in $${\mathbb {R}}^3$$R3, and prove that the rotationally symmetric bowl soliton is the only noncompact ancient solution of mean curvature flow in $${\mathbb {R}}^3$$R3 which is strictly convex and noncollapsed.
32 Citations
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