## 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 language | English (US) |
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Article number | 80 |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 58 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2019 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics