On immersions of constant mean curvature: Compactness results and finiteness theorems for Plateau's problem

DOI10.1007/BF00873495zbMath0753.53006OpenAlexW2000356272WikidataQ125573453 ScholiaQ125573453MaRDI QIDQ1812919

Friedrich Sauvigny

Publication date: 25 June 1992

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00873495

zbMATH Keywords

isoperimetric inequalityoscillation estimate

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Manifolds and measure-geometric topics (49Q99)

Related Items (8)

Finiteness of the number of solutions of Plateau's problem for polygonal boundary curves. II ⋮ Immersed solutions of Plateau's problem for piecewise smooth boundary curves with small total curvature ⋮ Local boundedness of the number of solutions of plateau's problem for polygonal boundary curves ⋮ Capillary surfaces in a convex cone ⋮ Finiteness of the set of solutions of Plateau's problem for polygonal boundary curves ⋮ Every ring type spanner in a wedge is spherical ⋮ A priori estimates of the principal curvatures for immersions of prescribed mean curvature and theorems of Bernstein-type ⋮ About the finiteness of the set of solutions of Plateau´s problem for polygonal boundary curves

Cites Work

• A priori estimates of the principal curvatures for immersions of prescribed mean curvature and theorems of Bernstein-type
• The 6\(\pi\) theorem about minimal surfaces
• Ein Eindeutigkeitssatz für Flächen konstanter mittlerer Krümmung
• The existence of embedded minimal surfaces and the problem of uniqueness
• Über die endliche Loesbarkeit des Plateau-Problems in Riemannschen Mannigfaltigkeiten
• A proof of a general isoperimetric inequality for surfaces
• On the local uniqueness of the problem of least area
• Zur Struktur der Lösungsmenge des Plateauproblems
• An inequality of isoperimetric type for surfaces of constant mean curvature
• Konstruktion isoperimetrischer Ungleichungen der mathematischen Physik aus solchen der Geometrie
• On the Size of a Stable Minimal Surface in R 3
• On the Local Behavior of Solutions of Non-Parabolic Partial Differential Equations
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