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Minimal surfaces of finite index in manifolds of positive scalar curvature

Part of the Lecture Notes in Mathematics book series (LNM,volume 1340)

Keywords

  • Minimal Surface
  • Scalar Curvature
  • Finite Index
  • Compact Riemann Surface
  • Jacobi Operator

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References

  1. S. Cohn-Vossen, Kürzeste Wege und Totalkrümmung auf Flächen, Compositio Math. 2 (1935), 69–133.

    MathSciNet  MATH  Google Scholar 

  2. A. Duschek, Zur geometrischen Variationsrechnung, Math. Z. 40 (1936), 279–291.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. D. Fischer-Colbrie, On complete minimal surfaces with finite Morse index, Inventiones Math. 82 (1985), 121–132.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. G. Gulliver, Index and total curvature of complete minimal surfaces, Proc. Symp. Pure Math. 44 (1986), 207–212.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. R. Gulliver and H.B. Lawson, The structure of stable minimal hypersurfaces near a singularity, Proc. Symp. Pure Math. 44 (1986), 213–237.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. H. Hardt, Topological properties of subanalytic sets, Trans. Amer. Math. Soc. 211 (1975), 57–70.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. H. Lewy, Aspects of the Calculus of Variations, University of California Press, Berkeley 1939.

    Google Scholar 

  8. R. Osserman, A survey of minimal surfaces, Van Nostrand-Reinhold, New York 1969.

    MATH  Google Scholar 

  9. R. Schoen, Uniqueness, symmetry and embeddedness of minimal surfaces, J. Differential Geom. 18 (1983), 791–809.

    MathSciNet  MATH  Google Scholar 

  10. R. Schoen and S.-T. Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with non-negative scalar curvature, Annals of Math. 110 (1979), 127–142.

    CrossRef  MathSciNet  MATH  Google Scholar 

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Dedicated to Hans Lewy

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© 1988 Springer-Verlag

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Gulliver, R. (1988). Minimal surfaces of finite index in manifolds of positive scalar curvature. In: Hildebrandt, S., Kinderlehrer, D., Miranda, M. (eds) Calculus of Variations and Partial Differential Equations. Lecture Notes in Mathematics, vol 1340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082890

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  • DOI: https://doi.org/10.1007/BFb0082890

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50119-0

  • Online ISBN: 978-3-540-45932-3

  • eBook Packages: Springer Book Archive