The Plateau problem at infinity for horizontal ends and genus 1
微分几何
2015-03-18 v1
摘要
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.
引用
@article{arxiv.math/0312080,
title = {The Plateau problem at infinity for horizontal ends and genus 1},
author = {Laurent Mazet},
journal= {arXiv preprint arXiv:math/0312080},
year = {2015}
}
备注
63 pages