TY - JOUR
T1 - On the characterization of minimal surfaces with finite total curvature in H 2 × R and PSL ~ 2 (R)
AU - Hauswirth, Laurent
AU - Menezes, Ana
AU - Rodríguez, Magdalena
N1 - Funding Information:
Research partially supported by the MCyT-FEDER research project MTM2014-52368-P, MTM2017-89677-P, and by the GENIL research project no. PYR-2014-21 of CEI BioTic GRANADA.
Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00526-019-1505-4
DO - 10.1007/s00526-019-1505-4
M3 - Article
AN - SCOPUS:85064060217
SN - 0944-2669
VL - 58
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 2
M1 - 80
ER -