Compact complete minimal immersions in ℝ³

DOI10.1090/S0002-9947-10-04741-0zbMath1196.53006arXiv0711.2394MaRDI QIDQ3581129

Antonio Alarcón

Publication date: 16 August 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.2394

zbMATH Keywords

complete minimal surfacesPlateau problem

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (9)

Every bordered Riemann surface is a complete conformal minimal surface bounded by Jordan curves: Figure. 5.1. ⋮ Compact complete null curves in complex 3-space ⋮ New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in ℝⁿ ⋮ Complete non-orientable minimal surfaces in \(\mathbb{R}^{3}\) and asymptotic behavior ⋮ Spectrum Estimates and Applications to Geometry ⋮ Null curves and directed immersions of open Riemann surfaces ⋮ Complete minimal surfaces in \(\mathbb R^3\) with a prescribed coordinate function ⋮ The Calabi-Yau problem for Riemann surfaces with finite genus and countably many ends ⋮ Isoperimetric inequalities for submanifolds. Jellett-Minkowski's formula revisited

Cites Work

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• Existence of proper minimal surfaces of arbitrary topological type
• A Jordan curve spanned by a complete minimal surface
• Adding handles to Nadirashvili's surfaces
• Density theorems for complete minimal surfaces in \({\mathbb{R}}^{3}\)
• The Calabi-Yau conjectures for embedded surfaces
• Limit sets for complete minimal immersions
• Complete proper minimal surfaces in convex bodies of \(\mathbb R^3\). II: The behavior of the limit set
• Bounded domains which are universal for minimal surfaces
• Solution of the Problem of Plateau
• On the asymptotic behavior of a complete bounded minimal surface in ℝ³
• Hadamard's and Calabi-Yau's conjectures on negatively curved and minimal surfaces

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