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On minimal annuli in a slab

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Commentarii Mathematici Helvetici

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References

  • [1]L. Barbosa andM. Do Carmo, On the size of a stable minimal surface in ℝ3. Amer. J. of Math.,98: 515–28, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  • [2]I. Chavel,Eigenvalues in Riemannian Geometry. Academic Press, Inc. Orlando, San Diego, New York, London, Montreal, Sydney, Tokyo, 1984.

    MATH  Google Scholar 

  • [3]Y. Fang,Lectures on Minimal Surface of Annular Type. Lecture Notes in A.N.U. Canberra, Australia.

  • [4]D. Hoffman, H. Karcher andH. Rosenberg, Embedded minimal annuli in ℝ3 bounded by a pair of straight lines. Comment. Math. Helvetici,66: 599–617, 1991.

    MathSciNet  MATH  Google Scholar 

  • [5]D. Hoffman andW. Meeks III,The asymptotic behavior of properly embedded minimal surfaces of finite topology. Journal of the Amer. Math. Soc.,2(4): 667–82, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  • [6]S. B. Jackson,Vertices for plane curves. Bull. of Amer. Math. Soc.,50: 564–78, 1944.

    Article  MATH  Google Scholar 

  • [7]L. P. Jorge andW. Meeks III,The topology of complete minimal surfaces of finite total Gaussian curvature. Topology,20(2): 203–21, 1983.

    Article  MathSciNet  Google Scholar 

  • [8]W. Meeks III andB. White.Minimal surfaces bounded by convex curves in parallel planes. Comment. Math. Helvetici,66: 263–78, 1991.

    MathSciNet  MATH  Google Scholar 

  • [9]J. C. C. Nitsche,Lectures on Minimal Surfaces, Vol. 1. Cambridge University Press, Cambridge, New York, New Rochelle, Melbourne, Sydney, 1989.

    Google Scholar 

  • [10]R. Osserman,A Survey of Minimal Surfaces, Dover Publishers, New York, 2nd edition, 1986.

    Google Scholar 

  • [11]M. Shiffman,On surfaces of stationary area bounded by two circles, or convex curves, in parallel planes. Annals of Math.,63: 77–90, 1956.

    Article  MathSciNet  Google Scholar 

  • [12]E. Toubiana,On the minimal surfaces of Riemann, Comment. Math. Helvetici,67: 546–70, 1992.

    Article  MathSciNet  MATH  Google Scholar 

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1991Mathematics Subject Classification Primary 53A10; Secondary 35P99. The research described in this paper is supported by Australia Research Council grant A688 30148. The author would like to thank the referee for pointing out mistakes in the previous version.

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Fang, Y. On minimal annuli in a slab. Commentarii Mathematici Helvetici 69, 417–430 (1994). https://doi.org/10.1007/BF02564495

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