Optimal regularity for codimension one minimal surfaces with a free boundary

DOI10.1007/BF01165891zbMath0609.35012OpenAlexW156929693MaRDI QIDQ1086741

Michael Grüter

Publication date: 1987

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155224

zbMATH Keywords

minimal surfacesfree boundarygeometric measure theoryinterior regularityHausdorff- dimensionreflection argumentsset of singular pointssingular minimizing conesvarifolds with free boundaries

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear boundary value problems for linear elliptic equations (35J65) 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 (20)

Weak solutions of inverse mean curvature flow for hypersurfaces with boundary ⋮ The relative isoperimetric inequality in Cartan-Hadamard 3-manifolds ⋮ The relative isoperimetric inequality outside convex domains in \(\mathbb{R}^{n}\) ⋮ Embedded solutions for exterior minimal surface problems ⋮ Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones ⋮ On the shape of capillarity droplets in a container ⋮ Free boundary problems for minimal surfaces and related questions ⋮ Min-max theory for free boundary minimal hypersurfaces. II: General Morse index bounds and applications ⋮ The Riemannian Penrose inequality for asymptotically flat manifolds with non-compact boundary ⋮ Multiplicity one for min-max theory in compact manifolds with boundary and its applications ⋮ Generalized soap bubbles and the topology of manifolds with positive scalar curvature ⋮ Min-max theory for minimal hypersurfaces with boundary ⋮ Min-max theory for free boundary minimal hypersurfaces. I: Regularity theory ⋮ Minimal hypersurfaces and bordism of positive scalar curvature metrics ⋮ Dirac and Plateau billiards in domains with corners ⋮ Dimensional estimates for singular sets in geometric variational problems with free boundaries ⋮ Front propagation in geometric and phase field models of stratified media ⋮ A note on the singular set of area-minimizing hypersurfaces ⋮ A two-piece property for free boundary minimal surfaces in the ball ⋮ Regularity of free boundaries in anisotropic capillarity problems and the validity of Young's law

Cites Work

• On the oriented Plateau problem
• On the first variation of a varifold: Boundary behavior
• Minimal varieties in Riemannian manifolds
• Minimal cones and the Bernstein problem
• On the first variation of a varifold
• The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension
• 𝑄 valued functions minimizing Dirichlet’s integral and the regularity of area minimizing rectifiable currents up to codimension two
• Boundary regularity and embedded solutions for the oriented Plateau problem
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