The alexandrov problem in a quotient space of ℍ2×ℝ

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Abstract

We prove an Alexandrov-type theorem for a quotient space of ℍ2×ℝ. More precisely, we classify the compact embedded surfaces with constant mean curvature in the quotient of ℍ2×R by a subgroup of isometries generated by a horizontal translation along horocycles of ℍ2 and a vertical translation. We also construct some examples of periodic minimal surfaces in ℍ2×ℝ and we prove a multivalued Rado theorem for small perturbations of the helicoid in ℍ2×ℝ.

Original languageEnglish (US)
Pages (from-to)155-172
Number of pages18
JournalPacific Journal of Mathematics
Volume268
Issue number1
DOIs
StatePublished - Jan 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Alexandrov reflection
  • Constant mean curvature surface
  • Periodic surface

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