Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group

Jih Hsin Cheng, Hung Lin Chiu, Jenn Fang Hwang, Paul Yang

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We study immersed, connected, umbilic hypersurfaces in the Heisenberg group Hn with n≥ 2. We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.

Original languageEnglish (US)
Article number66
JournalCalculus of Variations and Partial Differential Equations
Volume55
Issue number3
DOIs
StatePublished - Jun 1 2016

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • 32V20
  • 49Q10
  • 53A10
  • Primary 35L80
  • Secondary 35J70

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