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

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

2008-04-30

arxiv.org/abs/0804.4778v2

Mathematics

Differential Geometry

12 pages, 1 figure

Scientific paper

Consider a strictly convex bounded regular domain $C$ of $\R^3$. 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 $X:\overline{M}\to \overline{C}$.

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