Minimal surfaces with the area growth of two planes: The case of infinite symmetry

DOI10.1090/S0894-0347-06-00537-6zbMath1115.53008arXivmath/0501110OpenAlexW1892873315MaRDI QIDQ3420414

William Hamilton III Meeks, Michael Wolf

Publication date: 2 February 2007

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

Full work available at URL: https://arxiv.org/abs/math/0501110

zbMATH Keywords

quadratic area growthlimit tangent conearea growth constant

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15)

Related Items (10)

Scherk saddle towers of genus two in \({\mathbb R^3}\) ⋮ The Lawson surfaces are determined by their symmetries and topology ⋮ Catenoid limits of singly periodic minimal surfaces with Scherk-type ends ⋮ A Carleman inequality on product manifolds and applications to rigidity problems ⋮ MINIMAL HYPERSURFACES ASYMPTOTIC TO SIMONS CONES ⋮ Classification of the solutions to an overdetermined elliptic problem in the plane ⋮ A criterion for uniqueness of tangent cones at infinity for minimal surfaces ⋮ The classical theory of minimal surfaces ⋮ Multiple end solutions to the Allen-Cahn equation in \(\mathbb{R}^2\) ⋮ Ends, fundamental tones, and capacities of minimal submanifolds via extrinsic comparison theory

Cites Work

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• Uniqueness of the Riemann minimal examples
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• The geometry of periodic minimal surfaces
• An embedded minimal surface with no symmetries
• Classification of doubly-periodic minimal surfaces of genus zero
• Teichmüller theory and handle addition for minimal surfaces
• The classification of singly periodic minimal surfaces with genus zero and Scherk-type ends
• Weierstrass representation of some simply-periodic minimal surfaces

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