Slab theorem and halfspace theorem for constant mean curvature surfaces in H2 X R

Laurent Hauswirth, Ana Menezes, Magdalena Rodríguez

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that a properly embedded annular end of a surface in H2 X R with constant mean curvature 0 < H ≤ 1=2 can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature 0 < H ≤ 1=2 contained in H2 X Œ0; C1/ and with finite topology is necessarily a graph over a simply connected domain of H2. For the case H D 1=2, the graph is entire.

Original languageEnglish (US)
Pages (from-to)307-320
Number of pages14
JournalRevista Matematica Iberoamericana
Volume39
Issue number1
DOIs
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics

Keywords

  • Constant mean curvature surface
  • halfspace theorem
  • slab theorem

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