Bifurcation of minimal surfaces in Riemannian manifolds

Jost, Jürgen; Li-Jost, Xianqing; Peng, Xiao Wei

doi:10.1090/S0002-9947-1995-1270663-2

Bifurcation of minimal surfaces in Riemannian manifolds
HTML articles powered by AMS MathViewer

by Jürgen Jost, Xianqing Li-Jost and Xiao Wei Peng PDF

Trans. Amer. Math. Soc. 347 (1995), 51-62 Request permission

Correction: Trans. Amer. Math. Soc. 349 (1997), 4689-4690.

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

Th. Bröcker, Differentiable germs and catastrophes, London Mathematical Society Lecture Note Series, No. 17, Cambridge University Press, Cambridge-New York-Melbourne, 1975. Translated from the German, last chapter and bibliography by L. Lander. MR 0494220, DOI 10.1017/CBO9781107325418
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, DOI 10.1007/BF01185204
Joachim Büch, Bifurkation von Minimalflächen und elementare Katastrophen, Manuscripta Math. 55 (1986), no. 3-4, 269–306 (German, with English summary). MR 836867, DOI 10.1007/BF01186648
N. Hingston, Equivariant Morse theory and closed geodesics, J. Differential Geom. 19 (1984), no. 1, 85–116. MR 739783, DOI 10.4310/jdg/1214438424
Wilhelm Klingenberg, Lectures on closed geodesics, Grundlehren der Mathematischen Wissenschaften, Vol. 230, Springer-Verlag, Berlin-New York, 1978. MR 0478069, DOI 10.1007/978-3-642-61881-9
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

Untersuchung über zweidimensionale reguläre Variationsprobleme

Eindeutigkeit und Verzweigung von Minimalflächen