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Bifurcation of minimal surfaces in Riemannian manifolds
Author(s):
Jürgen
Jost;
Xianqing
Li-Jost;
Xiao Wei
Peng
Journal:
Trans. Amer. Math. Soc.
347
(1995),
51-62.
MSC:
Primary 58E20;
Secondary 53C22, 58E10
Correction(s):
Trans. Amer. Math. Soc. 349 (1997), 4689-4690.
MathSciNet review:
1270663
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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.
References:
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- [BR]
- Th. Bröcker, Differentiable germs and catastrophes, London Math. Soc. Lecture Note Ser. no. 17, Cambridge University Press, London and New York, 1975. MR 0494220 (58:13132)
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- M.J. Beeson and A.T. Tromba, The cusp catastrophe of Thom in the bifurcation of minimal surfaces, Manuscripta Math. 46 (1984), 273-308. MR 735523 (85h:58042)
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- J. Büch, Bifurkation von Minimalflächen und Elementare Katastrophen, Manuscripta Math. 55 (1986), 269-306. MR 836867 (87i:58038)
- [HI]
- N. Hingston, Equivariant Morse theory and closed geodesics, J. Differential Geom. 19 (1984), 85-116. MR 739783 (85i:58036)
- [KL]
- W. Klingenberg, Lectures on closed geodesics, Springer-Verlag, Berlin, 1978. MR 0478069 (57:17563)
- [LA]
- H.B. Lawson, Lectures on minimal submanifolds, Vol. 1, Publish or Perish, Berkeley, CA, 1980. MR 576752 (82d:53035b)
- [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:
10.1090/S0002-9947-1995-1270663-2
PII:
S0002-9947-1995-1270663-2
Keywords:
Minimal submanifolds,
bifurcation
Copyright of article:
Copyright
1995,
American Mathematical Society
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