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The behavior of the extremal length function on arbitrary Riemann surface

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1468)

Keywords

  • Riemann Surface
  • Quasiconformal Mapping
  • Variational Formula
  • Complex Line
  • Compact Riemann Surface

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References

  1. R. D. M. Accola, Differentials and extremal length on Riemann surfaces, Proc. Nat. Acad. Sci. U. S. A. 46 (1960), 540–543.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. L. Ahlfors, “Conformal Invariants,” McGraw-Hill Inc., 1973.

    Google Scholar 

  3. F. Maitani, Variations of meromorphic differentials under quasiconformal deformations, J. Math. Kyoto Univ. 24 (1984), 49–66.

    MathSciNet  MATH  Google Scholar 

  4. H. L. Royden, The variation of harmonic differentials and their periods, in “Complex Analysis,” Birkhäuser Verlag, 1988, pp. 211–223.

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  5. M. Taniguchi, Square integrable harmonic differentials on arbitrary Riemann surfaces with a finite number of nodes, J. Math. Kyoto Univ. 25 (1985), 597–617.

    MathSciNet  MATH  Google Scholar 

  6. M. Taniguchi, Variational formulas on arbitrary Riemann surfaces under pinching deformation, 27 (1987), 507–530.

    MathSciNet  MATH  Google Scholar 

  7. M. Taniguchi, Supplements to my previous papers; a refinement and applications, 28 (1988), 81–86.

    MathSciNet  MATH  Google Scholar 

  8. M. Taniguchi, Abelian differentials with normal behavior and complex pinching deformation, 29 (1989), 45–56.

    MathSciNet  MATH  Google Scholar 

  9. M. Taniguchi, Pinching deformation of arbitrary Riemann surfaces and variational formulas for abelian differentials, in “Analytic function theory of one complex variable,” Longman Sci. Techn., 1989, pp. 330–345.

    Google Scholar 

  10. M. Taniguchi, A note on the second variational formulas of functionals on Riemann surfaces, Kodai Math. J. 12 (1989), 283–295.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. M. Taniguchi, On the singularity of the periods of abelian differentials with normal behavior under pinching deformation, J. Math. Kyoto Univ. (to appear).

    Google Scholar 

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© 1991 Springer-Verlag

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Taniguchi, M. (1991). The behavior of the extremal length function on arbitrary Riemann surface. In: Noguchi, J., Ohsawa, T. (eds) Prospects in Complex Geometry. Lecture Notes in Mathematics, vol 1468. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086192

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  • DOI: https://doi.org/10.1007/BFb0086192

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54053-3

  • Online ISBN: 978-3-540-47370-1

  • eBook Packages: Springer Book Archive