On the existence of a proper minimal surface in R³ with the conformal type of a disk

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The main goal of this paper is to show a counterexample to the following conjecture: Conjecture [Meeks, Sullivan]: If f:M→ R³ 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: Theorem: There exists χ: D R³, a conformal proper minimal immersion defined on the unit disk.