Duke Mathematical Journal

Continuity of relative hyperbolic spectral theory through metric degeneration

Jay Jorgenson and Rolf Lundelius

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

Article information

Source
Duke Math. J., Volume 84, Number 1 (1996), 47-81.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077243628

Digital Object Identifier
doi:10.1215/S0012-7094-96-08402-1

Mathematical Reviews number (MathSciNet)
MR1394748

Zentralblatt MATH identifier
0872.58062

Subjects
Primary: 58G25
Secondary: 11F72: Spectral theory; Selberg trace formula 58G26

Citation

Jorgenson, Jay; Lundelius, Rolf. Continuity of relative hyperbolic spectral theory through metric degeneration. Duke Math. J. 84 (1996), no. 1, 47--81. doi:10.1215/S0012-7094-96-08402-1. https://projecteuclid.org/euclid.dmj/1077243628


Export citation

References

  • [ABMNV] L. Alvarez-Gaume, J.-B. Bost, G. Moore, P. Nelson, and C. Vafa, Bosonization on higher genus Riemann surfaces, Comm. Math. Phys. 112 (1987), no. 3, 503–552.
  • [BK] A. A. Belavin and V. G. Knizhnik, Complex geometry and the theory of quantum strings, Soviet Phys. JETP 64 (1986), 214–228.
  • [BGV] N. Berline, E. Getzler, and M. Vergne, Heat kernels and Dirac operators, Grundlehren der Math. Wiss. [Fundamental Principles of Mathematical Sciences], vol. 298, Springer-Verlag, Berlin, 1992.
  • [C] I. Chavel, Eigenvalues in Riemannian geometry, Pure and Appl. Math., vol. 115, Academic Press Inc., Orlando, FL, 1984.
  • [CF] I. Chavel and E. Feldman, Spectra of manifolds less a small domain, Duke Math. J. 56 (1988), no. 2, 399–414.
  • [Ch] S. Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975), no. 3, 289–297.
  • [CC] B. Colbois and G. Courtois, Les valeurs propres inférieures à $\frac 14$ des surfaces de Riemann de petit rayon d'injectivité, Comment. Math. Helv. 64 (1989), no. 3, 349–362.
  • [Do] J. Dodziuk, Maximum principle for parabolic inequalities and the heat flow on open manifolds, Indiana Univ. Math. J. 32 (1983), no. 5, 703–716.
  • [F] J. D. Fay, Kernel functions, analytic torsion, and moduli spaces, Mem. Amer. Math. Soc. 96 (1992), no. 464, vi+123.
  • [He] D. A. Hejhal, Regular $b$-groups, degenerating Riemann surfaces, and spectral theory, Mem. Amer. Math. Soc. 88 (1990), no. 437, iv+138.
  • [HJL] J. Huntley, J. Jorgenson, and R. Lundelius, Continuity of small eigenfunctions on degenerating Riemann surfaces with hyperbolic cusps, Bol. Soc. Mat. Mexicana (3) 1 (1995), no. 2, 119–125.
  • [JL] J. Jorgenson and R. Lundelius, Convergence theorems for relative spectral functions on hyperbolic Riemann surfaces of finite volume, Duke Math. J. 80 (1995), no. 3, 785–819.
  • [La] S. Lang, Introduction to complex hyperbolic spaces, Springer-Verlag, New York, 1987.
  • [Lu] R. Lundelius, Asymptotics of the determinant of the Laplacian on hyperbolic surfaces of finite volume, Duke Math. J. 71 (1993), no. 1, 211–242.
  • [MS] H. P. McKean and I. M. Singer, Curvature and the eigenvalues of the Laplacian, J. Differential Geometry 1 (1967), no. 1, 43–69.
  • [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.
  • [Mü] W. Müller, Spectral theory for Riemannian manifolds with cusps and a related trace formula, Math. Nachr. 111 (1983), 197–288.
  • [OPS] B. Osgood, R. Phillips, and P. Sarnak, Extremals of determinants of Laplacians, J. Funct. Anal. 80 (1988), no. 1, 148–211.
  • [S] R. Seeley, Complex powers of an elliptic operator, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966), American Mathematical Society, Providence, R.I., 1967, pp. 288–307.
  • [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.