SINGLY-PERIODIC MINIMAL SURFACES IN ℍ2×ℝ

Title & Authors
SINGLY-PERIODIC MINIMAL SURFACES IN ℍ2×ℝ
Pyo, Jun-Cheol;

Abstract
We construct three kinds of complete embedded singly-periodic minimal surfaces in $\small{\mathbb{H}^2{\times}\mathbb{R}}$. 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 $\small{\mathbb{H}^2{\times}\mathbb{R}}$ by finite Scherk`s towers.
Keywords
complete minimal surface;singly-periodic surface;product space;
Language
English
Cited by
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