A sufficient condition for a critical point of a functional to be a minimum and its application to Plateau's problem

DOI10.1007/BF01457133zbMath0518.58012MaRDI QIDQ1054040

Anthony J. Tromba

Publication date: 1983

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

Full work available at URL: https://eudml.org/doc/163749

zbMATH Keywords

Hilbert manifoldPlateau problemMorse lemmanormal form for functional about critical point

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25)

Related Items

Unfolding bifurcations of an elliptic boundary value problem, The generalized Morse lemma and the Euler characteristic on Banach manifolds, Lagrangian mechanics without ordinary differential equations, Morse theory on Banach manifolds, On the Morse number of embedded and non-embedded minimal immersions spanning wires on the boundary of special bodies in \({\mathbb{R}}^ 3\), Parameterized splitting theorems and bifurcations for potential operators. I: Abstract theory, The cusp catastrophe of Thom in the bifurcation of minimal surfaces, 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 index theorem for classical minimal surfaces
• A new uniqueness theorem for minimal surfaces
• Morse theory on Hilbert manifolds
• On universal unfoldings of certain real functions on a Banach space
• Almost-Riemannian Structures on Banach Manifolds: The Morse Lemma and the Darboux Theorem
• On the number of simply connected minimal surfaces spanning a curve
• Solution of the Problem of Plateau