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Transactions of the American Mathematical Society

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Bifurcation of minimal surfaces in Riemannian manifolds


Authors: Jürgen Jost, Xianqing Li-Jost and Xiao Wei Peng
Journal: Trans. Amer. Math. Soc. 347 (1995), 51-62
MSC: Primary 58E20; Secondary 53C22, 58E10
DOI: https://doi.org/10.1090/S0002-9947-1995-1270663-2
Correction: Trans. Amer. Math. Soc. 349 (1997), 4689-4690.
MathSciNet review: 1270663
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the bifurcation of closed minimal surfaces in Riemannian manifolds through higher order variations of the area functional and relate it to elementary catastrophes.


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  • [BR] Th. Bröcker, Differentiable germs and catastrophes, Cambridge University Press, Cambridge-New York-Melbourne, 1975. Translated from the German, last chapter and bibliography by L. Lander; London Mathematical Society Lecture Note Series, No. 17. MR 0494220
  • [BT] M. J. Beeson and A. J. Tromba, The cusp catastrophe of Thom in the bifurcation of minimal surfaces, Manuscripta Math. 46 (1984), no. 1-3, 273–308. MR 735523, https://doi.org/10.1007/BF01185204
  • [BÜ] Joachim Büch, Bifurkation von Minimalflächen und elementare Katastrophen, Manuscripta Math. 55 (1986), no. 3-4, 269–306 (German, with English summary). MR 836867, https://doi.org/10.1007/BF01186648
  • [HI] N. Hingston, Equivariant Morse theory and closed geodesics, J. Differential Geom. 19 (1984), no. 1, 85–116. MR 739783
  • [KL] Wilhelm Klingenberg, Lectures on closed geodesics, Springer-Verlag, Berlin-New York, 1978. Grundlehren der Mathematischen Wissenschaften, Vol. 230. MR 0478069
  • [LA] H. Blaine Lawson Jr., Lectures on minimal submanifolds. Vol. I, Monografías de Matemática [Mathematical Monographs], vol. 14, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1977. MR 527121
    H. Blaine Lawson Jr., Lectures on minimal submanifolds. Vol. I, 2nd ed., Mathematics Lecture Series, vol. 9, Publish or Perish, Inc., Wilmington, Del., 1980. MR 576752
  • [LI] L. Lichtenstein, Untersuchung über zweidimensionale reguläre Variationsprobleme, Monatsh. Math. Phys. 28 (1917).
  • [LJ] X. Li-Jost, Eindeutigkeit und Verzweigung von Minimalflächen, Dissertation, Univ. Bonn.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1270663-2
Keywords: Minimal submanifolds, bifurcation
Article copyright: © Copyright 1995 American Mathematical Society