Title: The Plateau problem at infinity for horizontal ends and genus 1

Authors: Laurent Mazet

Issue: Volume 55 (2006), Issue 1, 15-64

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.