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Riemann surfaces of large genus and large λ1

Part of the Lecture Notes in Mathematics book series (LNM,volume 1339)

Keywords

  • Riemann Surface
  • Boundary Component
  • Positive Element
  • Compact Surface
  • Geodesic Segment

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References

  1. P. Buser, Cubic graphs and the first eigenvalue of a Riemann surface, Math. Z. 162 (1978), 87–99.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. P. Buser, On the bipartition of graphs, Discrete Applied Mathematics, 9 (1984), 105–109.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. L. Bers, F. John, M. Schechter, Partial Differential Equations, AMS, Providence, RI 1979.

    MATH  Google Scholar 

  4. A.F. Beardon, The Geometry of Discrete Groups, Springer-Verlag, New York 1983.

    CrossRef  MATH  Google Scholar 

  5. S. Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975), 289–297.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. D.B.A. Epstein, Curves on 2-manifolds and isotopies, Acta Math. 115 (1966), 83–107.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. H. Jacquet, R. Langlands, Automorphic Forms on GL (2), Lect. Notes in Math. 114, Springer-Verlag, Berlin 1970.

    CrossRef  Google Scholar 

  8. J. Dodziuk, B. Randol, Lower bounds for λ1 on a finite volume hyperbolic manifold, J. Differential Geometry, 24 (1986), 133–139.

    MathSciNet  MATH  Google Scholar 

  9. J. Dodziuk, T. Pignataro, B. Randol, D. Sullivan, Estimating small eigenvalues of Riemann surfaces, Contemporary Mathematics 64, (1987), 93–121.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. A. Selberg, On the estimation of Fourier coefficients of modular forms, in Proceedings of Symposia in Pure Mathematics, vol. 8, AMS, Providence, RI 1965.

    Google Scholar 

  11. G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton University Press, Princeton NJ, 1971

    MATH  Google Scholar 

  12. R. Schoen, S. Wolpert, S.-T. Yau, Geometric bounds on low eigenvalues of a compact surface, in Geometry of Laplace Operator, AMS (1980), 279–285.

    Google Scholar 

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© 1988 Springer-Verlag

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Buser, P., Burger, M., Dodziuk, J. (1988). Riemann surfaces of large genus and large λ1 . In: Sunada, T. (eds) Geometry and Analysis on Manifolds. Lecture Notes in Mathematics, vol 1339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083046

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  • DOI: https://doi.org/10.1007/BFb0083046

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50113-8

  • Online ISBN: 978-3-540-45930-9

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