Uniqueness of convex ancient solutions to mean curvature flow in $${\mathbb {R}}^3$$ R 3
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Author(s)
Brendle, Simon
Choi, Kyeongsu
Date Issued
January 23, 2019
Publisher
Springer Berlin Heidelberg
Version
Author's final manuscript
Abstract
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
$$\kappa $$
κ
-noncollapsed. In this paper, we solve the analogous problem for mean curvature flow in
$${\mathbb {R}}^3$$
R
3
, and prove that the rotationally symmetric bowl soliton is the only noncompact ancient solution of mean curvature flow in
$${\mathbb {R}}^3$$
R
3
which is strictly convex and noncollapsed.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00222-019-00859-4
