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The cusp catastrophe of thom in the bifurcation of minimal surfaces

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References

  1. Böhme, R. and Tromba, A.J.; “The index theorem for classical minimal surfaces”, Annals of Math. 113 (1981), pp.447–499

    Google Scholar 

  2. Douglas, J.; “Solution to the problem of Plateau”, Trans Amer. Math. Soc. 33 (1931), pp.263–321

    Google Scholar 

  3. Gromoll, D. and Meyer, W.; “On differentiable functions with isolated critical points”, Top 8 (1969), pp.361–369

    Google Scholar 

  4. Nitsche, J.C.C.; “Vorlesungen über Minimalflächen”, Springer Verlag, Berlin,Heidelberg,New York, 1975

    Google Scholar 

  5. Nitsche, J.C.C.; “Contours bounding at least three solutions of Plateau's problem”, Arch. Rat. Mech. Anal. 30 (1968), pp.1–11

    Google Scholar 

  6. Nitsche, J.C.C.;“Non-uniqueness for Plateau's Problem. A Bifurcation Process”, Annales Academiae Scientiarum Fennicae, Volume 2 (1976), pp.361–373

    Google Scholar 

  7. Poston, T.; “The Problem of Plateau, an Introduction to the whole of Mathematics”, Mimeographical Notes-Summer Conference Trieste 1971

  8. Poston, T. and Stewart; Catastrophe Theory and Its Applications, Pitman, London 1978

    Google Scholar 

  9. Radó, T.; “On the Problem of Plateau”, Springer Verlag, Berlin, 1933

    Google Scholar 

  10. Ruchert, H.; “A uniqueness result for Enneper's minimal surface”, preprint

  11. Tomi, F.; “On the local uniqueness of the problem of least area”, Archive for Rational Mechanics and Analysis, Vol. 52, 4, (1973), pp.312–318

    Google Scholar 

  12. Tromba, A.J.; “A sufficient condition for a critical point to be a minimum and its applications to Plateau's problem”, (to appear in Mathematische Annalen)

  13. Tromba, A.J.; “On the number of simply connected minimal surfaces spanning a curve”, AMS Memoirs 194, November 1977

  14. Tromba, A.J.; “Almost Riemannian structures on Danach manifolds, the Morse lemma and the Darboux theorem”, Can. J. Math 28, (1976), pp.640–652

    Google Scholar 

  15. Zeeman, C.; “Catastrophe theory”, Selected papers, Addison-Wesley

Download references

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Authors and Affiliations

  1. Max-Planck-Institut für Mathematik, Gottfried-Claren-Straße 26, D-5300, Bonn 3

    M. J. Beeson & A. J. Tromba

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  1. M. J. Beeson
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  2. A. J. Tromba
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Research supported by the National Science Foundation and SFB 72, BONN

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Beeson, M.J., Tromba, A.J. The cusp catastrophe of thom in the bifurcation of minimal surfaces. Manuscripta Math 46, 273–308 (1984). https://doi.org/10.1007/BF01185204

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