An Extrinsic Rigity Theorem for Minimal Surfaces in S3.
An-Min Li (1985)
Mathematische Zeitschrift
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An-Min Li (1985)
Mathematische Zeitschrift
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Gerhard Dziuk (1985)
Mathematische Zeitschrift
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Francisco J. López, Francisco Martín (1999)
Publicacions Matemàtiques
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In this paper we review some topics on the theory of complete minimal surfaces in three dimensional Euclidean space.
Reinhold Böhme (1981-1982)
Séminaire Bourbaki
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Jürgen Jost (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Liu, Huili (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Shing-Tung Yau, William W. Meeks (1982)
Mathematische Zeitschrift
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Gianfranco Cimmino (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Simple computations support the conjecture that a small spherical surface with its center on a minimal surface cannot be divided by the minimal surface into two portions with different area.
K. Leschke, K. Moriya (2016)
Complex Manifolds
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In this paper we give a survey of methods of Quaternionic Holomorphic Geometry and of applications of the theory to minimal surfaces. We discuss recent developments in minimal surface theory using integrable systems. In particular, we give the Lopez–Ros deformation and the simple factor dressing in terms of the Gauss map and the Hopf differential of the minimal surface. We illustrate the results for well–known examples of minimal surfaces, namely the Riemann minimal surfaces and the...
Michael Beeson (1980)
Mathematische Zeitschrift
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Alexander G. Reznikov (1992)
Publicacions Matemàtiques
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We show that the apparatus of support functions, usually used in convex surfaces theory, leads to the linear equation Δh + 2h = 0 describing locally germs of minimal surfaces. Here Δ is the Laplace-Beltrami operator on the standard two-dimensional sphere. It explains the existence of the sum operator of minimal surfaces, introduced recently. In 4-dimensional space the equation Δ h + 2h = 0 becomes inequality wherever the Gauss curvature of a minimal hypersurface is nonzero.
H. Karcher (1988)
Manuscripta mathematica
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