On the existence of a proper minimal surface in $R^3$ with the conformal type of a disk
Abstract
Description
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 $χ: D\longrightarrow \mathbb{R}^3$, a conformal proper minimal immersion defined on the unit disk.
23 pages, 4 figures
23 pages, 4 figures