Singly-periodic minimal surfaces in $\Bbb H^2\times \Bbb R$
Bull. Korean Math. Soc. 2012 Vol. 49, No. 5, 1089-1099
https://doi.org/10.4134/BKMS.2012.49.5.1089
Printed September 30, 2012
Juncheol Pyo
Pusan National University
Abstract : We construct three kinds of complete embedded singly-peri\-odic minimal surfaces in $\Bbb H^2\times \Bbb R$. The first one is a 1-parameter family of minimal surfaces which is asymptotic to a horizontal plane and a vertical plane; the second one is a 2-parameter family of minimal surfaces which has a fundamental piece of finite total curvature and is asymptotic to a finite number of vertical planes; the last one is a 2-parameter family of minimal surfaces which fill $\Bbb H^2\times \Bbb R$ by finite Scherk's towers.
Keywords : complete minimal surface, singly-periodic surface, product space
MSC numbers : Primary 53C42; Secondary 53A35, 53C40
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