The Gauss map of pseudo-algebraic minimal surfaces in R4

DOI10.1002/mana.200610732zbMath1167.53009arXivmath/0603320OpenAlexW2012466068MaRDI QIDQ3615507

Yu Kawakami

Publication date: 20 March 2009

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603320

zbMATH Keywords

minimal surfaceGauss maptotally ramified value number

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Compact Riemann surfaces and uniformization (30F10) Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35)

Related Items (4)

Remarks on the Gauss images of complete minimal surfaces in Euclidean four-space ⋮ Value distribution of the Gauss map of improper affine spheres ⋮ Ramification of the Gauss map of complete minimal surfaces in \(\mathbb{R}^3\) and \(\mathbb{R}^4\) on annular ends ⋮ Non-integrated defect relations for the Gauss maps of complete minimal surfaces with finite total curvature

Cites Work

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• On subharmonic functions and differential geometry in the large
• On the totally ramified value number of the Gauss map of minimal surfaces
• On the number of exceptional values of the Gauss map of minimal surfaces
• On the Gauss map and total curvature of complete minimal surfaces and an extension of Fujimoto's theorem
• On the image of the generalized Gauss map of a complete minimal surface in \(R^ 4\).
• On the Gauss curvature of minimal surfaces
• Unicity theorems for the Gauss maps of complete minimal surfaces
• Algebraic curves and the Gauss map of algebraic minimal surfaces
• Gauss Map of Minimal Surfaces with Ramifiction
• The geometry of the generalized Gauss map

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