Asymptotics of the determinant of the Laplacian on hyperbolic surfaces of finite volume
Rolf E. Lundelius
Source: Duke Math. J. Volume 71, Number 1
(1993), 211-242.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077289842
Mathematical Reviews number (MathSciNet): MR1230291
Zentralblatt MATH identifier: 0790.58044
Digital Object Identifier: doi:10.1215/S0012-7094-93-07109-8
References
[Ab] W. Abikoff, The Real Analytic Theory of Teichmüller Space, Lecture Notes in Math., vol. 820, Springer-Verlag, Berlin, 1980.
Mathematical Reviews (MathSciNet): MR82a:32028
Zentralblatt MATH: 0452.32015
[Br] L. Bers, Spaces of degenerating Riemann surfaces, Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973), Princeton Univ. Press, Princeton, N.J., 1974, 43–55. Ann. of Math. Studies, No. 79.
Mathematical Reviews (MathSciNet): MR50:13497
Zentralblatt MATH: 0294.32016
[CH] R. Courant and D. Hilbert, Methods of Mathematical Physics, Volume 1, Interscience Publishers, New York, 1953.
Mathematical Reviews (MathSciNet): MR16,426a
Zentralblatt MATH: 0053.02805
[Ch] I. Chavel, Eigenvalues in Riemannian Geometry, Pure Appl. Math., vol. 115, Academic Press, Orlando, 1984.
Mathematical Reviews (MathSciNet): MR86g:58140
Zentralblatt MATH: 0551.53001
[DPRS] J. Dodziuk, T. Pignataro, B. Randol, and D. Sullivan, Estimating small eigenvalues of Riemann surfaces, The legacy of Sonya Kovalevskaya (Cambridge, Mass., and Amherst, Mass., 1985), Contemp. Math., vol. 64, Amer. Math. Soc., Providence, RI, 1987, pp. 93–121.
Mathematical Reviews (MathSciNet): MR88h:58119
Zentralblatt MATH: 0607.58044
[Fo] G. B. Folland, Introduction to Partial Differential Equations, Math. Notes, Princeton University Press, Princeton, 1976.
Mathematical Reviews (MathSciNet): MR58:29031
Zentralblatt MATH: 0325.35001
[He] D. A. Hejhal, The Selberg trace formula for $\rm PSL(2,\,\bf R)$. Vol. 2, Lecture Notes in Mathematics, vol. 1001, Springer-Verlag, Berlin, 1983.
Mathematical Reviews (MathSciNet): MR86e:11040
Zentralblatt MATH: 0543.10020
[Ka] M. Kac, Can One Hear the Shape of a Drum? Amer. Math. Monthly 73 (1966), no. 4, part II, 1–23.
Mathematical Reviews (MathSciNet): MR34:1121
Zentralblatt MATH: 0139.05603
Digital Object Identifier: doi:10.2307/2313748
[MS] H. P. McKean and I. M. Singer, Curvature and the Eigenvalues of the Laplacian, J. Differential Geom. 1 (1967), no. 1, 43–69.
Mathematical Reviews (MathSciNet): MR36:828
Zentralblatt MATH: 0198.44301
Project Euclid: euclid.jdg/1214427880
[MP] S. Minakshisundaram and A. Pleijel, Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242–256.
Mathematical Reviews (MathSciNet): MR11,108b
Zentralblatt MATH: 0041.42701
[Mu] W. Müller, Spectral theory for Riemannian manifolds with cusps and a related trace formula, Math. Nachr. 111 (1983), 197–288.
Mathematical Reviews (MathSciNet): MR85i:58121
Zentralblatt MATH: 0529.58035
Digital Object Identifier: doi:10.1002/mana.19831110109
[OPS] B. Osgood, R. Phillips, and P. Sarnak, Extremals of determinants of Laplacians, J. Funct. Anal. 80 (1988), no. 1, 148–211.
Mathematical Reviews (MathSciNet): MR90d:58159
Zentralblatt MATH: 0653.53022
Digital Object Identifier: doi:10.1016/0022-1236(88)90070-5
[PW] M. Protter and H. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall Partial Differential Equations Ser., Prentice-Hall, Englewood Cliffs, New Jersey, 1967.
Mathematical Reviews (MathSciNet): MR36:2935
Zentralblatt MATH: 0549.35002
[Sm] L. Smith, The asymptotics of the heat equation for a boundary value problem, Invent. Math. 63 (1981), no. 3, 467–493.
Mathematical Reviews (MathSciNet): MR82m:35117
Zentralblatt MATH: 0487.35012
Digital Object Identifier: doi:10.1007/BF01389065
[SWY] 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.
Mathematical Reviews (MathSciNet): MR81i:58052
Zentralblatt MATH: 0446.58018
[Va] S. R. S. Varadhan, On the behavior of the fundamental solution of the heat equation with variable coefficients, Comm. Pure Appl. Math. 20 (1967), 431–455.
Mathematical Reviews (MathSciNet): MR34:8001
Zentralblatt MATH: 0155.16503
Digital Object Identifier: doi:10.1002/cpa.3160200404
[Wo] S. A. Wolpert, Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces, Comm. Math. Phys. 112 (1987), no. 2, 283–315.
Mathematical Reviews (MathSciNet): MR89c:58136
Zentralblatt MATH: 0629.58029
Digital Object Identifier: doi:10.1007/BF01217814
Project Euclid: euclid.cmp/1104159880
[Wl] A. Weil, Elliptic Functions according to Eisenstein and Kronecker, Ergeb. Math. Grenzgeb., vol. 88, Springer-Verlag, Berlin, 1976.
Mathematical Reviews (MathSciNet): MR58:27769a
Zentralblatt MATH: 0318.33004
Duke Mathematical Journal
