Foliations of hyperbolic space by constant mean curvature surfaces sharing ideal boundary

David Chopp, John A. Veiling

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let γ be a Jordan curve in 8 2, considered as the ideal boundary of H3. Under certain circumstances, it is known that for any c ϵ (-1, 1), there is a disc of constant mean curvature c embedded in H3 with γ as its ideal boundary. Using analysis and numerical experiments, we examine whether or not these surfaces in fact foliate H3, and to what extent the known conditions on the curve can be relaxed.

Original languageEnglish (US)
Pages (from-to)339-350
Number of pages12
JournalExperimental Mathematics
Volume12
Issue number3
DOIs
StatePublished - 2003

Keywords

  • Constant mean curvature
  • Foliations
  • Hyperbolic space
  • Level set method

ASJC Scopus subject areas

  • Mathematics(all)

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