Translating solitons in arbitrary codimension
type: Item
instance of: scholarly article
title: Translating solitons in arbitrary codimension
zbMATH Open document ID: 1383.53007
author: Keita Kunikawa
published in: The Asian Journal of Mathematics
publication date: 2018-02-12T00:00:00Z
review text: Mean curvature flow has finite-time singularities in general which are classified into two categories: Type I and Type II. It is known that by rescaling at a singularity, we obtain a self-shrinker as a limiting submanifold of Type I and an eternal solution as a limiting submanifold of Type II. Translating solitons are important examples of eternal solutions, which do not change their shape under the mean curvature flow up to translation in Euclidean space. Although many authors study translating solitons in codimension one, there are few references and examples for higher-codimensional cases except for Lagrangian translating solitons. In this paper, the author first observes non-trivial examples of translating solitons in arbitrary codimension. Inspired by the fact that they have the property called parallel principal normal and the work of \textit{K. Smoczyk} for self-shrinkers in [Int. Math. Res. Not. 2005, No. 48, 2983--3004 (2005; Zbl 1085.53059)], the author characterizes the complete translating solitons with the above property.
reviewed by: Atsushi Fujioka
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53C44
zbMATH DE Number: 6837105
zbMATH Keywords: mean curvature flow
zbMATH Keywords: translating soliton
zbMATH Keywords: parallel principal normal
MaRDI profile type: Publication
full work available at URL: ajm.2017.v21.n5.a4
OpenAlex ID: W2789558348
DOI: 10.4310/AJM.2017.V21.N5.A4
description: scientific article; zbMATH DE number 6837105