Some recent developments in the theory of properly embedded minimal surfaces in
Harold Rosenberg (1991-1992)
Séminaire Bourbaki
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Displaying similar documents to “Complete minimal surfaces in R3.”
Some recent developments in the theory of properly embedded minimal surfaces in
New results on the classical problem of Plateau on the existence of many solutions
Reinhold Böhme (1981-1982)
Séminaire Bourbaki
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A rigidity theorem for Riemann's minimal surfaces
Pascal Romon (1993)
Annales de l'institut Fourier
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We describe first the analytic structure of Riemann’s examples of singly-periodic minimal surfaces; we also characterize them as extensions of minimal annuli bounded by parallel straight lines between parallel planes. We then prove their uniqueness as solutions of the perturbed problem of a punctured annulus, and we present standard methods for determining finite total curvature periodic minimal surfaces and solving the period problems.
Existence results for embedded minimal surfaces of controlled topological type, I
Jürgen Jost (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Curvature estimates for minimal surfaces in -manifolds
Michael T. Anderson (1985)
Annales scientifiques de l'École Normale Supérieure
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Existence results for embedded minimal surfaces of controlled topological type, III
Jürgen Jost (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Linearization and explicit solutions of the minimal surface equations.
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.