On the asymptotic behavior of a complete bounded minimal surface in ℝ³

DOI10.1090/S0002-9947-04-03451-8zbMath1057.53009OpenAlexW1756212634MaRDI QIDQ4813836

Francisco Martín, Santiago Morales

Publication date: 13 August 2004

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-04-03451-8

zbMATH Keywords

Euclidean 3-spacebounded complete minimal surfaces

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) Optimization of shapes other than minimal surfaces (49Q10)

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Complete proper minimal surfaces in convex bodies of \(\mathbb R^3\) ⋮ Existence of proper minimal surfaces of arbitrary topological type ⋮ NEW COMPLEX ANALYTIC METHODS IN THE THEORY OF MINIMAL SURFACES: A SURVEY ⋮ Limit sets for complete minimal immersions ⋮ ON MINIMAL SURFACES SATISFYING THE OMORI–YAU PRINCIPLE ⋮ Compact complete minimal immersions in ℝ³ ⋮ The halfspace theorem for minimal hypersurfaces in regions bounded by minimal cones

Cites Work

• The strong halfspace theorem for minimal surfaces
• Convex hulls of complete minimal surfaces
• Adding handles to Nadirashvili's surfaces
• On the existence of a proper minimal surface in \(\mathbb R^3\) with a conformal type of disk
• A complete bounded minimal cylinder in \(\mathbb R^3\)
• Hadamard's and Calabi-Yau's conjectures on negatively curved and minimal surfaces