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arXiv · 1711.00823

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

S. Brendle·K. Choi
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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 $κ$-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.

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S. Brendle, K. Choi. 2019-01-14. Uniqueness of convex ancient solutions to mean curvature flow in $\mathbb{R}^3$. https://arxiv.org/abs/1711.00823

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