Properness of associated minimal surfaces

DOI10.1090/S0002-9947-2014-06050-9zbMath1298.53011arXiv1203.0751OpenAlexW2122329296WikidataQ125852495 ScholiaQ125852495MaRDI QIDQ3190795

Antonio Alarcón, Francisco J. López

Publication date: 19 September 2014

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

Full work available at URL: https://arxiv.org/abs/1203.0751

zbMATH Keywords

associated minimal surfacesnull holomorphic curves

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (8)

Embedded minimal surfaces in \(\mathbb R^n\) ⋮ The Calabi-Yau problem, null curves, and Bryant surfaces ⋮ Holomorphic Legendrian curves ⋮ NEW COMPLEX ANALYTIC METHODS IN THE THEORY OF MINIMAL SURFACES: A SURVEY ⋮ Complete non-orientable minimal surfaces in \(\mathbb{R}^{3}\) and asymptotic behavior ⋮ Minimal surfaces in minimally convex domains ⋮ Null Holomorphic Curves in $$\mathbb{C}^{3}$$ and Applications to the Conformal Calabi-Yau Problem ⋮ Approximation theory for nonorientable minimal surfaces and applications

Cites Work

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• Minimal surfaces in \(\mathbb{R}^3\) properly projecting into \(\mathbb{R}^2\)
• Algebraic curves and non rigid minimal surfaces in the Euclidean space
• On the existence of a proper minimal surface in \(\mathbb R^3\) with a conformal type of disk
• Complete minimal surfaces and harmonic functions
• Null curves in \({\mathbb{C}^3}\) and Calabi-Yau conjectures
• Immersion of open Riemann surfaces
• Uniform approximation by complete minimal surfaces of finite total curvature in ℝ³

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