On the existence of a proper minimal surface in $R^3$ with the conformal type of a disk

Santiago Morales

On the existence of a proper minimal surface in $R^3$ with the conformal type of a disk

Differential Geometry 2007-05-23 v1

Authors: Santiago Morales

Abstract

The main goal of this paper is to show a counterexample to the following conjecture: {\bf Conjecture} [Meeks, Sullivan]: If $f:M\to \mathbb{R}^3$ is a complete proper minimal immersion where $M$ is a Riemannian surface without boundary and with finite genus, then $M$ is parabolic. We have proved: {\bf Theorem:} There exists $\chi: D\longrightarrow \mathbb{R}^3$ , a conformal proper minimal immersion defined on the unit disk.

Keywords

minimal surface proper immersion conformal type Riemannian surface parabolic counterexample

Cite

@article{arxiv.math/0301132,
  title  = {On the existence of a proper minimal surface in $R^3$ with the conformal type of a disk},
  author = {Santiago Morales},
  journal= {arXiv preprint arXiv:math/0301132},
  year   = {2007}
}

Comments

23 pages, 4 figures

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