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

Laurent Hauswirth; Ana Menezes; Magdalena Rodríguez

doi:10.1007/s00526-019-1505-4

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

Laurent Hauswirth, Ana Menezes, Magdalena Rodríguez

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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)
Article number	80
Journal	Calculus of Variations and Partial Differential Equations
Volume	58
Issue number	2
DOIs	https://doi.org/10.1007/s00526-019-1505-4
State	Published - Apr 1 2019

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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Hauswirth, L., Menezes, A., & Rodríguez, M. (2019). On the characterization of minimal surfaces with finite total curvature in H ² × R and PSL ~ ₂ (R) Calculus of Variations and Partial Differential Equations, 58(2), [80]. https://doi.org/10.1007/s00526-019-1505-4

Hauswirth, Laurent ; Menezes, Ana ; Rodríguez, Magdalena. / On the characterization of minimal surfaces with finite total curvature in H ² × R and PSL ~ ₂ (R) In: Calculus of Variations and Partial Differential Equations. 2019 ; Vol. 58, No. 2.

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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. ",

author = "Laurent Hauswirth and Ana Menezes and Magdalena Rodr{\'i}guez",

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Hauswirth, L, Menezes, A & Rodríguez, M 2019, ' On the characterization of minimal surfaces with finite total curvature in H ² × R and PSL ~ ₂ (R) ', Calculus of Variations and Partial Differential Equations, vol. 58, no. 2, 80. https://doi.org/10.1007/s00526-019-1505-4

On the characterization of minimal surfaces with finite total curvature in H ² × R and PSL ~ ₂ (R) . / Hauswirth, Laurent; Menezes, Ana; Rodríguez, Magdalena.

In: Calculus of Variations and Partial Differential Equations, Vol. 58, No. 2, 80, 01.04.2019.

Research output: Contribution to journal › Article › peer-review

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Hauswirth L, Menezes A, Rodríguez M. On the characterization of minimal surfaces with finite total curvature in H ² × R and PSL ~ ₂ (R) Calculus of Variations and Partial Differential Equations. 2019 Apr 1;58(2). 80. https://doi.org/10.1007/s00526-019-1505-4