Plateau's problem and Riemann's mapping theorem

DOI10.1007/s00032-011-0142-yzbMath1282.49031OpenAlexW2041194281WikidataQ126087972 ScholiaQ126087972MaRDI QIDQ640706

Stefan Hildebrandt

Publication date: 19 October 2011

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-011-0142-y

zbMATH Keywords

areaminimal surfacesDirichlet integralPlateau's problemmapping theorems of Riemann and Koebe

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items (1)

Some geometric properties of nonparametric \(\mu\)-surfaces in \(\mathbb{R}^3\)

Cites Work

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• Relative minimizers of energy are relative minimizers of area
• On Lichtenstein's theorem about globally conformal mappings
• Minimal Surfaces
• Regularity of Minimal Surfaces
• Global Analysis of Minimal Surfaces
• Conformal mappings and the Plateau-Douglas problem in Riemannian manifolds.
• INTRODUCTION OF ISOTHERMAL PARAMETERS INTO A RIEMANNIAN METRIC BY THE CONTINUITY METHOD
• Conformal mapping of multiply connected Riemann domains by a variational approach

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