# 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} }

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

Rotational symmetry of ancient solutions to mean curvature flow in $\mathbb{R}^3$

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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.… Expand

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In a recent paper [2], we obtained a classification of noncompact ancient solutions in R3 which are convex and noncollapsed. The proof of Theorem 1.1 draws on similar techniques. In Section 2, we… Expand

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