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The asymptotic behavior of green’s functions for quasi-hyperbolic metrics on degenerating Riemann surfaces

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References

  1. Fay, J.: Theta functions on Riemann surfaces. Lecture notes in Math.352. Berlin-Heideberg-New York: Springer 1973

    Google Scholar 

  2. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin-Heidelberg-New York: Springer 1977

    MATH  Google Scholar 

  3. Hejhal, D.: Regularb-groups, degenerating Riemann surfaces and spectrial theory. Memoirs of Amer. Math. Soc.88, No. 437, 1990

    Google Scholar 

  4. Ji, L.: The asymptotic behavior of Green’s functions for degenerating hyperbolic surfaces. Math. Z.212, 375–394 (1993)

    Article  MATH  Google Scholar 

  5. Ji, L.: Spectral degeneration of hyperbolic Riemann surfaces. J. Diff. Geom.38, 263–313 (1993)

    MATH  Google Scholar 

  6. Jorgenson, J.: Asymptotic behavior of Faltings’ delta function. Duke Math. J.61, 221–254 (1990)

    Article  MATH  Google Scholar 

  7. Lang, S.: Introduction to Arakelov theory. Berlin-Heidelberg-New York: Springer 1988

    MATH  Google Scholar 

  8. Schoen, R., Wolpert, S., Yau, S.T.: Geometric bounds on the low eigenvalues of a compact surface. Proc. Symp. Pure Math.36, 279–285 (1980)

    Google Scholar 

  9. Wentworth, R.: The asymptotics of the Arakelov-Green’s function and Faltings’ delta invariant. Commun. Math. Phys.137, 427–459 (1991)

    Article  MATH  Google Scholar 

  10. Wolpert, S.: Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces. Commun. Math. Phys.112, 283–315 (1987)

    Article  MATH  Google Scholar 

  11. Wolpert, S.: The hyperbolic metric and the geometry of the universal curve. J. Diff. Geom.31, 417–472 (1990)

    MATH  Google Scholar 

  12. Yau, S. T.: A general Schwarz lemma for Kähler manifolds. Amer. J. Math.100, 199–203 (1978)

    Article  Google Scholar 

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To, WK., Weng, L. The asymptotic behavior of green’s functions for quasi-hyperbolic metrics on degenerating Riemann surfaces. Manuscripta Math 93, 465–480 (1997). https://doi.org/10.1007/BF02677486

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