Displaying similar documents to “Berger's Isoperimetric Problem and Minimal Immersions of Surfaces.”

Complete minimal surfaces in R.

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.

On Veronese-Borůvka spheres

Katsuei Kenmotsu (1997)

Archivum Mathematicum

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In this paper, history of reserches for minimal immersions from constant Gaussian curvature 2-manifolds into space forms is explained with special emphasis of works of O. Borůvka. Then recent results for the corresponding probrem to classify minimal immersions of such surfaces in complex space forms are discussed.

A conjecture on minimal surfaces

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.

Applications of Quaternionic Holomorphic Geometry to minimal surfaces

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...