Bernstein-type theorem of translating solitons in arbitrary codimension with flat normal bundle

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We give a proof for a Bernstein-type theorem of complete graphs of translating solitons in higher codimension. In the case of hypersurfaces, Bao–Shi showed that a translating soliton whose image of the Gauss map is contained in a compact subset in an open hemisphere is a hyperplane. This means that there is no nontrivial translating soliton whose slope is bounded. In the present article, we generalize this theorem in arbitrary codimension. Moreover we obtain an optimal growth condition which allows unbounded slopes. As a corollary, our result covers a classical Bernstein-type theorem for minimal submanifolds.

Original languageEnglish
Pages (from-to)1331-1344
Number of pages14
JournalCalculus of Variations and Partial Differential Equations
Volume54
Issue number2
DOIs
Publication statusPublished - 2015 Oct 22

Keywords

  • 53A07
  • 53C25
  • 53C42
  • 53J05

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Bernstein-type theorem of translating solitons in arbitrary codimension with flat normal bundle'. Together they form a unique fingerprint.

Cite this