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The behavior of the extremal length function on arbitrary Riemann surface

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Prospects in Complex Geometry

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

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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.

    Article  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.

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  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.

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

    Article  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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Authors and Affiliations

  1. Department of Mathematics, Kyoto university, 606, Kyoto, Japan

    Masahiko Taniguchi

Authors
  1. Masahiko Taniguchi
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Junjiro Noguchi Takeo Ohsawa

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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

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