Plateau's problem for H-convex curves

DOI10.1007/BF01277607zbMath0678.49030MaRDI QIDQ1124103

Fang-Hua Lin

Publication date: 1987

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

Full work available at URL: https://eudml.org/doc/155234

zbMATH Keywords

uniquenessminimal surfacesnon-uniqueness``top and ``bottom solutionsstable, embedded minimal disk

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)

Related Items (4)

Mean convex hulls and least area disks spanning extreme curves ⋮ Generic uniqueness of least area planes in hyperbolic space ⋮ On the convexity of geometric functionals of level for solutions of certain elliptic partial differential equations ⋮ On a class of minimal hypersurfaces in \(\mathbb{R}^ n\)

Cites Work

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• Stationary partitioning of convex bodies
• The existence of embedded minimal surfaces and the problem of uniqueness
• A perturbation theorem for surfaces of constant mean curvature
• On the first variation of a varifold: Boundary behavior
• Curvature estimates for minimal hypersurfaces
• On embedded minimal surfaces
• Plateau's problem for embedded minimal surfaces of the type of the disc
• A survey of the geometric results in the classical theory of minimal surfaces
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Stable complete minimal surfaces in 𝑅³ are planes
• On the Size of a Stable Minimal Surface in R 3

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