On doubly periodic minimal surfaces in H2× R with finite total curvature in the quotient space

Laurent Hauswirth, Ana Menezes

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

In this paper, we develop the theory of properly immersed minimal surfaces in the quotient space (H2× R) / G, where G is a subgroup of isometries generated by a vertical translation and a horizontal isometry (without fixed points) in H2. The horizontal isometry can be either a parabolic translation along horocycles in H2 or a hyperbolic translation along a geodesic in H2. We prove that if a properly immersed minimal surface in (H2× R) / G has finite total curvature, then its total curvature is a multiple of 2 π and, moreover, we understand the geometry of the ends. The results hold true more generally for properly immersed minimal surfaces in M× S1, where M is a hyperbolic surface with finite topology whose ends are isometric to one of the ends of the above spaces (H2× R) / G.

Original languageEnglish (US)
Pages (from-to)1491-1512
Number of pages22
JournalAnnali di Matematica Pura ed Applicata
Volume195
Issue number5
DOIs
StatePublished - Oct 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Keywords

  • Finite total curvature
  • Holomorphic quadratic differential
  • Minimal surfaces

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