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Les valeurs propres inférieures à 1/4 des surfaces de Riemann de petit rayon d’injectivité

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Commentarii Mathematici Helvetici

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Bibliographie

  1. A. F. Beardon,The geometry of discrete groups, Springer Verlag, Berlin, 1983.

    MATH  Google Scholar 

  2. M. Burger,Dégénérescence de surface de Riemann et petites valuers propres, Preprint, Bâle, 1987.

  3. M. Burger, P. Buser etJ. Dodziuk, Riemann surfaces of large genus and large λ1, Preprint, 1987.

  4. P. Buser, On Cheeger inequality λ1h 2/4, Proc. of Symp. in Pure Math.36, pp. 29–77, 1980.

    MathSciNet  Google Scholar 

  5. P. Buser,Riemannsche Flächen und Längenspectrum vom trigonometrischen Standpunkt, Aus Habilitationsschrift, Bonn, 1980.

  6. I. Chavel,Eigenvalue in riemannian geometry, Academic Press, New York, 1984.

    Google Scholar 

  7. S. Y. Cheng,Eigenvalue comparison theorems and its geometric applications, Math. Z.143, 1975, pp. 289–297.

    Article  MathSciNet  Google Scholar 

  8. B. Colbois etY. Colin de Verdière,Sur la multiplicité de la première valeur propre d’une surface de Riemann à courbure constante, Prépublication de l’Institut, Fourier no. 62 (1986). A paraitre aux Comm. Math. Helv.

  9. B. Colbois,Petites valeurs propres du laplacien sur une surface de Riemann compacte et graphes, C. R. Acad. Sci. Paris301, 1985, pp. 927–930.

    MathSciNet  Google Scholar 

  10. B. Colbois,Sur la multiplicité de la première valeur propre non nulle du laplacien des surfaces à courbure-1, Thèse, Lausanne, 1987.

  11. R. Courant etD. Hilbert,Methods of Mathematical Physics, Wiley-Interscience I, 1953, II 1962.

  12. H. Donnelly,On the essential spectrum on a complete riemannian manifold, Topology20, pp. 1–14, 1981.

    Article  MathSciNet  Google Scholar 

  13. B. Randol,Cylinders in Riemann surfaces, Comm. Math. Helv.54, pp. 1–5, 1979.

    MathSciNet  Google Scholar 

  14. R. Schoen, S. Wolpert etS. T. Yau,Geometric bounds of the low eigenvalues of a compact surface Proc. symp. Pure Math.36, pp. 279–285, 1980.

    MathSciNet  Google Scholar 

  15. D. A. Hejhal, A continuity method for spectral theory on fuchsian groups in:Modular forms. Rankin, R. A. (ed), Ellis-Horwood (1984) pp. 107–140.

  16. D. A. Hejhal,Regular B-groups, degenerating Riemann surfaces and spectral theory, Preprint Chalmers University of Technology and the University of Göteborg (1987).

  17. Y. Colin de Verdière,Résonances, Séminaire de Théorie Spectrale et Géométrie, Université de Grenoble, Institut Fourier, 1984–85.

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

    Article  MathSciNet  Google Scholar 

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Durant l’élaboration de ce travail, le premier auteur bénéficiait d’une bourse de la Fondation Pierre Mercier.

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Colbois, B., Courtois, G. Les valeurs propres inférieures à 1/4 des surfaces de Riemann de petit rayon d’injectivité. Commentarii Mathematici Helvetici 64, 349–362 (1989). https://doi.org/10.1007/BF02564681

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  • DOI: https://doi.org/10.1007/BF02564681

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