Über Stabilität und Isoliertheit der Lösungen des klassischen Plateauproblems

DOI10.1007/BF01214794zbMath0396.53004OpenAlexW2913636294MaRDI QIDQ1253451

Reinhold Böhme

Publication date: 1978

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/172633

zbMATH Keywords

StabilityImplicit Function Theorem of Nash-Moser TypeIsolatednessMinimal Surfaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Nonlinear elliptic equations (35J60) Manifolds of mappings (58D15) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15)

Related Items

Eine globalanalytische Behandlung des Douglas'schen Problems. (A global analysis treatment of the Douglas problem), Degree theory on oriented infinite-dimensional varieties and the Morse number of minimal surfaces spanning a curve in \({\mathbb{R}}^ n\), C2 stability of curves with non-degenerate solution to Plateau's problem, Stabilität mehrfach zusammenhängender Minimalflächen, Ein Indexsatz für Flächen konstanter mittlerer Krümmung, Isoliertheit und Stabilität von Flächen konstanter mittlerer Krümmung, The number of solutions to the classical Plateau problem is generically finite, Plateau's problem for surfaces of constant mean curvature from a global point of view, Jacobifelder zu Flächen konstanter mittlerer Krümmung, Intrinsic third derivatives for Plateau's problem and the Morse inequalities for disc minimal surfaces in \(\mathbb{R}^ 3\)

Cites Work

• Die Jacobifelder zu Minimalflächen im \(\mathbb{R}^3\)
• Zur Struktur der Lösungsmenge des Plateauproblems
• The boundary behavior of minimal surfaces. Kellogg's theorem and branch points on the boundary
• Un théorème de fonctions implicites sur certains espaces de Fréchet et quelques applications
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