Translating solitons in arbitrary codimension

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Abstract

We study the translating solitons of the mean curvature flow. Although many authors study translating solitons in codimension one, there are few references and examples for higher codimensional cases except for Lagrangian translating solitons. First we observe non-trivial examples of translating solitons in arbitrary codimension. We will see that they have the property called parallel principal normal (PPN). Inspired by this fact and the work of Smoczyk for selfshrinkers in 2005, we then characterize the complete translating solitons with PPN.

Original languageEnglish
Pages (from-to)855-872
Number of pages18
JournalAsian Journal of Mathematics
Volume21
Issue number5
DOIs
Publication statusPublished - 2017

Keywords

  • Mean curvature flow
  • Parallel principal normal
  • Translating soliton

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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