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The Plateau problem at infinity for horizontal ends and genus 1

Laurent Mazet
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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.

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Laurent Mazet. 2003-12-03. The Plateau problem at infinity for horizontal ends and genus 1. https://doi.org/10.1512/iumj.2006.55.2583

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