On the Gauss map and total curvature of complete minimal surfaces and an extension of Fujimoto's theorem

DOI10.4310/JDG/1214444316zbMath0666.53003OpenAlexW1563569788WikidataQ115182290 ScholiaQ115182290MaRDI QIDQ1116462

Xiaokang Mo, Robert Osserman

Publication date: 1990

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

Full work available at URL: https://doi.org/10.4310/jdg/1214444316

zbMATH Keywords

minimal surfacefinite total curvatureGauss map

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (12)

On complete minimal surfaces whose Gauss map misses two directions ⋮ Modified defect relations of the Gauss map and the total curvature of a complete minimal surface ⋮ Construction of minimal annuli in \(\widetilde{\mathrm{PSL}}_2(\mathbb{R},\tau)\) via a variational method ⋮ On complete space-like stationary surfaces in 4-dimensional Minkowski space with graphical Gauss image ⋮ Ramification of the Gauss map and the total curvature of a complete minimal surface ⋮ Ramification of the Gauss map of complete minimal surfaces in \(\mathbb{R}^3\) and \(\mathbb{R}^4\) on annular ends ⋮ On values of Gauss maps of complete minimal surfaces on annular ends ⋮ The Gauss map of pseudo-algebraic minimal surfaces in R⁴ ⋮ Some Picard theorems for minimal surfaces ⋮ Modified defect relations for the gauss map of minimal surfaces, III ⋮ Properly embedded minimal annuli in \(\mathbb{H}^2 \times \mathbb{R}\) ⋮ Non-integrated defect relations for the Gauss maps of complete minimal surfaces with finite total curvature

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