Compact complete proper minimal immersions in strictly convex bounded regular domains of R^3

Abstract

Consider a strictly convex bounded regular domain $C$ of ${\mathbb{R}}^3$. For any arbitrary finite topological type we find a compact Riemann surface $\mathcal{M}$, an open domain $M\subset \mathcal{M}$ with the fixed topological type, and a conformal complete proper minimal immersion $X:M\to C$ which can be extended to a continuous map $X:\overline{M}\to \overline{C}$.

12 pages, 1 figure