Convex solutions to the mean curvature flow
type: Item
instance of: scholarly article
title: Convex solutions to the mean curvature flow
zbMATH Open document ID: 1231.53058
published in: Annals of Mathematics. Second Series
publication date: 2011-10-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0404326
review text: An open problem related to the classification of type II singularities is whether a convex translating solution is \(k\)--rotationally symmetric for some integer \(2 \leq k \leq n\), namely whether its level set is a sphere or a cylinder. The author gives an affirmative answer for entire solutions in dimension 2. In high dimensions it is also proved that there exist nonrotationally symmetric, entire convex translating solutions, but the blow-down in space of any entire convex translating solution is \(k\)--rotationally symmetric and that the blow-down in space-time of an ancient convex solution which sweeps the whole space \(\mathbb R^{n+1}\) is a shrinking sphere or cylinder. The author surveys new progress made in this field, after this paper was finished in early 2003.
reviewed by: Gheorghe Pitiş
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 5960683
zbMATH Keywords: ancient convex solution
zbMATH Keywords: mean curvature flow
zbMATH Keywords: rotationally symmetric solution
author: Xu-Jia Wang
MaRDI profile type: Publication
OpenAlex ID: W2119790810
arXiv ID: math/0404326
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DOI: 10.4007/ANNALS.2011.173.3.1
description: scientific article