Boundary regularity and embedded solutions for the oriented Plateau problem

DOI10.1090/S0273-0979-1979-14581-6zbMath0421.49042OpenAlexW2170060381WikidataQ61458453 ScholiaQ61458453MaRDI QIDQ5904194

Leon Simon, Robert M. Hardt

Publication date: 1979

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-1979-14581-6

zbMATH Keywords

minimal surfacetangent coneexcessboundary regularityplateau problemembedded solutionsabsolutely area minimizing rectifiable current

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

Related Items

A survey of the geometric results in the classical theory of minimal surfaces ⋮ Inverse mean curvature flow of rotationally symmetric hypersurfaces ⋮ \(C^{1,\alpha }\) theory for the prescribed mean curvature equation with Dirichlet data ⋮ Soap film solutions to Plateau's problem

Cites Work

• On the first variation of a varifold: Boundary behavior
• Minimal cones and the Bernstein problem
• Asymptotic behavior and uniqueness of plane subsonic flows
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension
• Boundary regularity and embedded solutions for the oriented Plateau problem
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