Conformal mapping of multiply connected Riemann domains by a variational approach

DOI10.1515/ACV.2009.007zbMath1175.30012OpenAlexW2162163314MaRDI QIDQ5321863

Heiko von der Mosel, Stefan Hildebrandt

Publication date: 15 July 2009

Published in: ACV (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/acv.2009.007

zbMATH Keywords

conformal mappingmultiply connected domainminimizing sequenceRiemann domainDouglas conditionFrechét type convergenceplanar Douglas problem

Mathematics Subject Classification ID

Variational inequalities (49J40) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) General theory of conformal mappings (30C35) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (9)

Finiteness of the number of solutions of Plateau's problem for polygonal boundary curves. II ⋮ Conformal mappings of multiply connected domains onto canonical domains using the Green and Neumann functions ⋮ The plateau problem for the Busemann-Hausdorff area in arbitrary codimension ⋮ Plateau's problem and Riemann's mapping theorem ⋮ Sufficient conditions for Willmore immersions in \(\mathbb R^3\) to be minimal surfaces ⋮ Erratum to: ``Sufficient conditions for Willmore immersions in \(\mathbb R^3\) to be minimal surfaces ⋮ Plateau's problem in Finsler 3-space ⋮ Some geometric properties of nonparametric \(\mu\)-surfaces in \(\mathbb{R}^3\) ⋮ About the finiteness of the set of solutions of Plateau´s problem for polygonal boundary curves

Cites Work

• On two-dimensional parametric variational problems
• The Douglas problem for parametric double integrals
• On Lichtenstein's theorem about globally conformal mappings
• Ein einfacher Beweis eines Regularitätssatzes für schwache Lösungen gewisser elliptischer Systeme
• Minimal surfaces of higher topological structure
• The existence of minimal surfaces of given topological structure under prescribed boundary conditions
• The problem of Plateau on a Riemannian manifold
• Plateau's problem for parametric double integrals: I. Existence and regularity in the interior
• Some remarks on minimal surfaces in riemannian manifolds
• Semicontinuity problems in the calculus of variations

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