Proves that rotationally and reflection symmetric compact noncollapsed ancient 3D Ricci flow solutions are either spheres or have unique asymptotics as t to -∞ with explicit description.
Uniqueness of convex ancient solutions to mean curvature flow in $\mathbb{R}^3$
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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 $\kappa$-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.
fields
math.DG 2years
2019 2verdicts
UNVERDICTED 2representative citing papers
An expository paper that presents and simplifies Wang's structure theory for convex ancient mean curvature flow solutions and shows rigidity results follow from it, including a new corollary.
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Unique asymptotics of ancient compact non-collapsed solutions to the 3-dimensional Ricci flow
Proves that rotationally and reflection symmetric compact noncollapsed ancient 3D Ricci flow solutions are either spheres or have unique asymptotics as t to -∞ with explicit description.
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Convex ancient solutions to mean curvature flow
An expository paper that presents and simplifies Wang's structure theory for convex ancient mean curvature flow solutions and shows rigidity results follow from it, including a new corollary.