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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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