The cusp catastrophe of Thom in the bifurcation of minimal surfaces

DOI10.1007/BF01185204zbMath0551.58005OpenAlexW2003062020MaRDI QIDQ801341

Michael J. Beeson, Anthony J. Tromba

Publication date: 1984

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

Full work available at URL: https://eudml.org/doc/155000

zbMATH Keywords

bifurcationcatastrophesPlateau's problemEnneper's surfaceDirichlet's integral

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Catastrophe theory (58K35)

Related Items (11)

Bifurkation von Minimalflächen und elementare Katastrophen. (Bifurcation of minimal surfaces and elementary catastrophes) ⋮ Bifurcation near solutions of variational problems with degenerate second variation ⋮ On the numerical approximation and computation of minimal surface continua bounded by one-parameter families of polygonal contours ⋮ Unfolding bifurcations of an elliptic boundary value problem ⋮ Bifurcations of minimal surfaces via index theory ⋮ Some results on finiteness in Plateau's problem. I ⋮ Morse lemma for functionals of variational calculus ⋮ Entropy, minimal surfaces and negatively curved manifolds ⋮ Bifurcation of Minimal Surfaces in Riemannian Manifolds ⋮ Intensionality in mathematics ⋮ The geometric invariants for mPCLP/mDCLP family

Cites Work

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• A sufficient condition for a critical point of a functional to be a minimum and its application to Plateau's problem
• The index theorem for classical minimal surfaces
• On the local uniqueness of the problem of least area
• Contours bounding at least three solutions of Plateau's problem
• On differentiable functions with isolated critical points
• Almost-Riemannian Structures on Banach Manifolds: The Morse Lemma and the Darboux Theorem
• Non-uniqueness for Plateau's problem. A bifurcation process
• On the number of simply connected minimal surfaces spanning a curve

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