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SINGLY-PERIODIC MINIMAL SURFACES IN ℍ2×ℝ

  • Pyo, Jun-Cheol (Department of Mathematics Pusan National University)
  • Received : 2011.07.06
  • Published : 2012.09.30

Abstract

We construct three kinds of complete embedded singly-periodic minimal surfaces in $\mathbb{H}^2{\times}\mathbb{R}$. 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 $\mathbb{H}^2{\times}\mathbb{R}$ by finite Scherk's towers.

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