The plateau problem at infinity for horizontal ends and genus 1

被引：6

作者：

Mazet, L ^{[1
]}

机构：

[1] Univ Toulouse 3, Lab Emile Picard, UMR 5580, F-31062 Toulouse, France

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2006年 / 55卷 / 01期

关键词：

minimal surface; Dirichlet problem; boundary behaviour; degree theory;

D O I：

10.1512/iumj.2006.55.2583

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study Alexandrov-embedded r-noids with genus I 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.

引用

页码：15 / 64

页数：50

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