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. 
Rotational symmetry of ancient solutions to mean curvature flow in $\mathbb{R}^3$
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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Translators asymptotic to cylinders
  • Or Hershkovits
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
  • 2019
Abstract We show that the Bowl soliton in ℝ 3 {\mathbb{R}^{3}} is the unique translating solution of the mean curvature flow whose tangent flow at - ∞ {-\infty} is the shrinking cylinder. As anExpand
Convex Ancient Solutions to Mean Curvature Flow
X.-J. Wang proved a series of remarkable results on the structure of convex ancient solutions to mean curvature flow. Some of his results do not appear to be widely known, however, possibly due toExpand
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