On the characterization of minimal surfaces with finite total curvature in H 2 × R and PSL ~ 2 (R)

Laurent Hauswirth, Ana Maria Menezes de Jesus, Magdalena Rodríguez

Research output: Contribution to journalArticle

Abstract

It is known that a complete immersed minimal surface with finite total curvature in H 2 × R is proper, has finite topology and each one of its ends is asymptotic to a geodesic polygon at infinity (Hauswirth and Rosenberg in Mat Contemp 31:65–80, 2006; Hauswirth et al. in Adv Math 274:199–240, 2015). In this paper we prove that these three properties characterize complete immersed minimal surfaces with finite total curvature in H 2 × R. As corollaries of this theorem we obtain characterizations for minimal Scherk-type graphs and horizontal catenoids in H 2 × R. We also prove that if a properly immersed minimal surface in PSL ~ 2 (R, τ) has finite topology and each one of its ends is asymptotic to a geodesic polygon at infinity, then it must have finite total curvature.

Original languageEnglish (US)
Article number80
JournalCalculus of Variations and Partial Differential Equations
Volume58
Issue number2
DOIs
StatePublished - Apr 1 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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