The Plateau problem at infinity for horizontal ends and genus 1

Abstract

In this paper, we study Alexandrov-embedded r-noids with genus 1 and horizontal ends. Such minimal surfaces are of two types and we build several examples of the first one. We prove that if a polygon bounds an immersed polygonal disk, it is the flux polygon of an r-noid with genus 1 of the first type. We also study the case of polygons which are invariant under a rotation. The construction of these surfaces is based on the resolution of the Dirichlet problem for the minimal surface equation on an unbounded domain.

63 pages

References in corpus (1)

• The Dirichlet problem for minimal surfaces equation and Plateau problem at infinity

Cited by in corpus (2)

• Conjugate Plateau constructions in product spaces
• Genus one minimal k-noids and saddle towers in ${\mathbb{H}}^2\times \mathbb{R}$