Unique asymptotics of ancient convex mean curvature flow solutions

By Sigurd B. Angenent, P. Daskalopoulos, N. Šešum. Journal of differential geometry, 2015

93 citations recorded by the source corpus.

We study the compact noncollapsed ancient convex solutions to Mean Curvature Flow in $\mathbb{R}^{n+1}$ with $O(1)\times O(n)$ symmetry. We show they all have unique asymptotics as $t\to -\infty$ and we give precise asymptotic description of these solutions. In particular, solutions constructed by White, and Haslhofer and Hershkovits have those asymptotics (in the case of those particular solutions the asymptotics was predicted and formally computed by Angenent).

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/48ca6b19053feb0169326fe5ce4e0f6efd83255a

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Uniqueness of compact ancient solutions to three-dimensional Ricci flow (2020, background): “In [2,3], it was shown that every ancient solution to mean curvature flow which is compact, noncollapsed, strictly convex, and uniformly two-convex is either the family of shrinking spheres or the family of”
Ancient solutions to the Ricci flow in dimension $3$ (2018, background): “As in [3] and [9], a subtle point here is that we need to control certain error terms arising from the cutoff functions.”
Uniqueness of convex ancient solutions to mean curvature flow in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\m (2018, methodology): “4 in [1], we obtain ua(2) ≤ √ 2(n− 1) and ua(2) − ua(1) ≤ −a−2 if a is sufficiently large.”