JournalscmhVol. 81, No. 3pp. 699–725

Complete proper minimal surfaces in convex bodies of <em><strong>R</strong><sup>3</sup></em>, II. The behavior of the limit set

  • Francisco Martín

    Universidad de Granada, Spain
  • Santiago Morales

    Universidad de Granada, Spain
Complete proper minimal surfaces in convex bodies of <em><strong>R</strong><sup>3</sup></em>, II. The behavior of the limit set cover
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Abstract

Let DD be a regular, strictly convex bounded domain of R3\mathbb{R}^3, and consider a Jordan curve ΓD\Gamma \subset \partial D. Then, for each ε>0\varepsilon>0, we obtain the existence of a complete proper minimal immersion ψε ⁣:DD\psi_\varepsilon \colon \mathbb{D} \rightarrow D satisfying that the Hausdorff distance δH(ψε(D),Γ)<ε,\delta^H(\psi_\varepsilon(\partial \mathbb{D}), \Gamma) < \varepsilon, where ψε(D)\psi_\varepsilon(\partial \mathbb{D}) represents the limit set of the minimal disk ψε(D)\psi_\varepsilon(\mathbb{D}).

Cite this article

Francisco Martín, Santiago Morales, Complete proper minimal surfaces in convex bodies of <em><strong>R</strong><sup>3</sup></em>, II. The behavior of the limit set. Comment. Math. Helv. 81 (2006), no. 3, pp. 699–725

DOI 10.4171/CMH/70