On the Gauss map of a complete minimal surface in \(R^ m\).

DOI10.2969/JMSJ/03520279zbMath0495.53004OpenAlexW2045427867MaRDI QIDQ1169690

Hirotaka Fujimoto

Publication date: 1983

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

Full work available at URL: https://doi.org/10.2969/jmsj/03520279

zbMATH Keywords

Nevanlinna theoryGauss mapPicard type 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) Value distribution theory in higher dimensions (32H30) Picard-type theorems and generalizations for several complex variables (32H25)

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Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into $\mathbb{P}^{n}(\mathbb{C})$ intersecting hypersurfaces ⋮ Non-integrated defect of meromorphic maps on Kähler manifolds ⋮ New Complex Analytic Methods in the Study of Non-Orientable Minimal Surfaces in ℝⁿ ⋮ Harmonic mappings and conformal minimal immersions of Riemann surfaces into \(\mathbb R^{\mathrm N}\) ⋮ Non-integrated defect relation for meromorphic mappings on Kähler manifolds intersecting non-subdegenerate families of hyperplanes ⋮ NEW COMPLEX ANALYTIC METHODS IN THE THEORY OF MINIMAL SURFACES: A SURVEY ⋮ Meromorphic mappings of a complete connected Kähler manifold into a projective space sharing hyperplanes ⋮ Algebraic relation of two meromorphic mappings on a Kähler manifold having the same inverse images of hyperplanes ⋮ Every meromorphic function is the Gauss map of a conformal minimal surface

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