  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.
