Complete minimal surfaces in Euclidean \(n\)-spaces
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Publication:2532103
DOI10.1007/BF02788707zbMath0172.22802OpenAlexW1756181857WikidataQ125853411 ScholiaQ125853411MaRDI QIDQ2532103
Robert Osserman, Shiing-shen Chern
Publication date: 1967
Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02788707
Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)
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Cites Work
- Unnamed Item
- On subharmonic functions and differential geometry in the large
- Minimal surfaces in the large
- Global properties of minimal surfaces in \(E^ 3\) and \(E^ n\)
- On a class of conformal metrics, with application to differential geometry in the large
- Eine Determinantenidentität und ihre Anwendung auf analytische Gebilde in euklidischer und Hermitescher Maßbestimmung
- Integral Geometry in Hermitian Spaces
- Meromorphic Functions and Analytic Curves. (AM-12)
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