Regularity of C 1 smooth surfaces with prescribed p-mean curvature in the Heisenberg group

Jih Hsin Cheng, Jenn Fang Hwang, Paul Chien-Ping Yang

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

We consider a C1 smooth surface with prescribed p (or H)-mean curvature in the 3-dimensional Heisenberg group. Assuming only the prescribed p-mean curvature H Ie{cyrillic, ukrainian} C0 we show that any characteristic curve is C2 smooth and its (line) curvature equals - H in the nonsingular domain. By introducing characteristic coordinates and invoking the jump formulas along characteristic curves, we can prove that the Legendrian (or horizontal) normal gains one more derivative. Therefore the seed curves are C2 smooth. We also obtain the uniqueness of characteristic and seed curves passing through a common point under some mild conditions, respectively. These results can be applied to more general situations.

Original languageEnglish (US)
Pages (from-to)1-35
Number of pages35
JournalMathematische Annalen
Volume344
Issue number1
DOIs
StatePublished - Feb 1 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

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

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