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arXiv · 0804.4778

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

Antonio Alarcon
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Abstract

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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Antonio Alarcon. 2008-11-19. Compact complete proper minimal immersions in strictly convex bounded regular domains of R^3. https://arxiv.org/abs/0804.4778

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