Minimal surfaces in \(\mathbb{R}^ 3\) and algebraic curves

DOI10.1016/0926-2245(92)90003-6zbMath0768.53004OpenAlexW2013734618WikidataQ115362777 ScholiaQ115362777MaRDI QIDQ1207170

Anthony J. Small

Publication date: 23 May 1993

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0926-2245(92)90003-6

zbMATH Keywords

Hirzebruch surfacefinite total Gaussian curvatureosculation dualityWeierstrass formulae

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Rational and birational maps (14E05)

Related Items (7)

OSCULATION AND SINGULARITY OF CHARGE 2 (COMPLEXIFIED) BPS MONOPOLES ⋮ Linear structures on the collections of minimal surfaces in \(\mathbb{R}^ 3\) and \(\mathbb{R}^ 4\) ⋮ On complete nonorientable minimal surfaces with low total curvature ⋮ Duality for a class of minimal surfaces \(\mathbb{R}^{n+1}\) ⋮ Formulae for null curves deriving from elliptic curves ⋮ Harmonic maps into the orthogonal group and null curves ⋮ Implicit equations of the Henneberg-type minimal surface in the four-dimensional Euclidean space

Cites Work

• A duality theorem for Willmore surfaces
• \(\text{SU}(2)\) monopoles of charge \(2\)
• Complete minimal surfaces and minimal herissons
• The classification of complete minimal surfaces in \(R^ 3\) with total curvature greater than -8pi
• Monopoles and geodesics
• Concerning my paper on the boundary behavior of minimal surfaces
• Minimal curves in six dimensions
• Witten identities for rotations, spinor boundary-value problems and new gauge conditions for asymptotic symmetries
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