Degree theory on oriented infinite-dimensional varieties and the Morse number of minimal surfaces spanning a curve in \({\mathbb{R}}^ n\)

DOI10.1007/BF01169005zbMath0622.58006MaRDI QIDQ1090997

Anthony J. Tromba

Publication date: 1984

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

Full work available at URL: https://eudml.org/doc/155023

zbMATH Keywords

minimal surfacesmountain-pass lemmaMorse number

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15)

Related Items (5)

Quasi-linear elliptic differential equations for mappings of manifolds. II ⋮ Min-max theory for minimal hypersurfaces with boundary ⋮ Variational methods in geometry ⋮ H-surface index formula ⋮ Intrinsic third derivatives for Plateau's problem and the Morse inequalities for disc minimal surfaces in \(\mathbb{R}^ 3\)

Cites Work

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• The Euler characteristic of vector fields on Banach manifolds and a globalization of Leray-Schauder degree
• Über Stabilität und Isoliertheit der Lösungen des klassischen Plateauproblems
• Boundary behavior of 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
• The Plateau problem for non-relative minima
• Corrections to our paper on the existence of minimal surfaces of general critical types
• Degree Theory on Oriented Infinite Dimensional Varieties and the Morse Number of Minimal Surfaces Spanning a Curve in R n . Part I: n ≥4
• On the number of solutions to Plateau’s problem
• The number of solutions to the classical Plateau problem is generically finite
• An Infinite Dimensional Version of Sard's Theorem

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