JournalscmhVol. 81 , No. 3DOI 10.4171/cmh/70

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

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}).