Modified defect relations for the Gauss map of minimal surfaces

DOI10.4310/JDG/1214442873zbMath0676.53005OpenAlexW4237960087WikidataQ115182842 ScholiaQ115182842MaRDI QIDQ1122786

Hirotaka Fujimoto

Publication date: 1989

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/jdg/1214442873

zbMATH Keywords

Nevanlinna theoryminimal surfacesGauß mapDefect relationsfour-points-theorem

Mathematics Subject Classification ID

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

Related Items (13)

Nevanlinna theory for minimal surfaces of parabolic type ⋮ An estimate for the Gaussian curvature of minimal surfaces in \(\mathbb R^m\) whose Gauss map is ramified over a set of hyperplanes ⋮ Modified defect relations of the Gauss map and the total curvature of a complete minimal surface ⋮ The value distribution of the hyperbolic Gauss map ⋮ Ramification of the Gauss map of complete minimal surfaces in \(\mathbb{R}^3\) and \(\mathbb{R}^4\) on annular ends ⋮ Hyperbolic complete minimal surfaces with arbitrary topology ⋮ A Bernstein type theorem for minimal volume preserving maps ⋮ Modified defect relations for the gauss map of minimal surfaces, III ⋮ On the uniqueness of the helicoid and Enneper’s surface in the Lorentz-Minkowski space $\mathbb \{R\}\textunderscore \{1\}^\{3\}$ ⋮ Curvature estimates for minimal submanifolds of higher codimension ⋮ A Bernstein type result of translating solitons ⋮ Non-integrated defect relations for the Gauss maps of complete minimal surfaces with finite total curvature ⋮ Unicity theorems for the Gauss maps of complete minimal surfaces. II

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