Plateau's problem for embedded minimal surfaces of the type of the disc

DOI10.1007/BF01226463zbMath0399.53002MaRDI QIDQ1254739

Friedrich Tomi

Publication date: 1978

Published in: Archiv der Mathematik (Search for Journal in Brave)

zbMATH Keywords

Disc TypeEmbedded Minimal SurfacesHilbert Manifold ApproachPlateau's Problem

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Spaces of embeddings and immersions (58D10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items

A survey of the geometric results in the classical theory of minimal surfaces, Plateau's problem for H-convex curves, The existence of embedded minimal surfaces and the problem of uniqueness, On the Morse number of embedded and non-embedded minimal immersions spanning wires on the boundary of special bodies in \({\mathbb{R}}^ 3\), The index theorem for \(k\)-fold connected minimal surfaces

Cites Work

• On embedded minimal surfaces
• A proof of the regularity everywhere of the classical solution to Plateau's problem
• Regularity of minimizing surfaces of prescribed mean curvature
• Verzweigungspunkte von H-Flächen. I
• Verzweigungspunkte von H-Flächen. II
• On boundary branch points of minimizing surfaces
• The existence of minimal surfaces of given topological structure under prescribed boundary conditions
• A Theory of Branched Immersions of Surfaces
• Minimal Surfaces of General Topological Structure with Any Finite Number of Assigned Boundaries
• Unnamed Item
• Unnamed Item