Complete proper minimal surfaces in convex bodies of $\mathbb R^3$, II. The behavior of the limit set

• Autores: Francisco Martín Serrano, Santiago Morales
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 81, Nº 3, 2006, págs. 699-725
• Idioma: inglés
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• Resumen

  • Let $D$ be a regular, strictly convex bounded domain of $\mathbb{R}^3$, and consider a Jordan curve $\Gamma \subset \partial D$. Then, for each $\varepsilon>0$, we obtain the existence of a complete proper minimal immersion $\psi_\varepsilon \colon \mathbb{D} \rightarrow D$ satisfying that the Hausdorff distance $\delta^H(\psi_\varepsilon(\partial \mathbb{D}), \Gamma) < \varepsilon,$ where $\psi_\varepsilon(\partial \mathbb{D})$ represents the limit set of the minimal disk $\psi_\varepsilon(\mathbb{D})$.