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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Asymptotics of small eigenvalues of Riemann surfaces


Author: Marc Burger
Journal: Bull. Amer. Math. Soc. 18 (1988), 39-40
MSC (1985): Primary 53C22, 58G25; Secondary 30F99
MathSciNet review: 919656
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References [Enhancements On Off] (What's this?)

  • Marc Burger, Estimation de petites valeurs propres du laplacien d’un revêtement de variétés riemanniennes compactes, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 5, 191–194 (French, with English summary). MR 832070 (87f:58164)
  • Marc Burger, Spectre du laplacien, graphes et topologie de Fell, Comment. Math. Helv. 63 (1988), no. 2, 226–252 (French). MR 948779 (89h:58193), http://dx.doi.org/10.1007/BF02566764
  • Peter Buser, Cubic graphs and the first eigenvalue of a Riemann surface, Math. Z. 162 (1978), no. 1, 87–99. MR 505920 (80b:58061), http://dx.doi.org/10.1007/BF01437826
  • [Bu2] P. Buser, Riemannsche Flächen und Längenspektrum vom trigonometrischen Standpunkt aus, Habilitationsschrift, Bonn, 1980.
  • [C.CdV] B. Colbois and Y. Colin de Verdière, Sur la multiplicité de la première valeur propre d'une surface de Riemann à courbure constante, preprint.
  • [D.P.R.S.] J. Dodziuk, T. Pignataro, B. Randol, and D. Sullivan, Estimating small eigenvalues of Riemann surfaces, preprint.
  • R. Schoen, S. Wolpert, and S. T. Yau, Geometric bounds on the low eigenvalues of a compact surface, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979) Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 279–285. MR 573440 (81i:58052)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1988-15588-7
PII: S 0273-0979(1988)15588-7