Duke Mathematical Journal

Isospectral sets of conformally equivalent metrics

Robert Brooks, Peter Perry, and Paul Yang

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

Duke Math. J. Volume 58, Number 1 (1989), 131-150.

First available in Project Euclid: 20 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58G25
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 58G11


Brooks, Robert; Perry, Peter; Yang, Paul. Isospectral sets of conformally equivalent metrics. Duke Math. J. 58 (1989), no. 1, 131--150. doi:10.1215/S0012-7094-89-05808-0. http://projecteuclid.org/euclid.dmj/1077307376.

Export citation


  • [A] T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampère Equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 252, Springer-Verlag, New York, 1982.
  • [Be] M. Berger, P. Gauduchon, and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Mathematics, vol. 194, Springer-Verlag, Berlin, 1971.
  • [Br] R. Brooks, On manifolds of negative curvature with isospectral potentials, Topology 26 (1987), no. 1, 63–66.
  • [Br-T] R. Brooks and R. Tse, Isospectral surfaces of small genus, Nagoya Math. J. 107 (1987), 13–24.
  • [C-Y] S. Y. A. Chang and P. Yang, Compactness of isospectral conformal metrics on $S^3$, to appear in Comm. Math. Helv.
  • [G] P. Gilkey, Leading terms in the asymptotics of the heat equation, preprint.
  • [O-P-S] B. Osgood, R. Phillips, and P. Sarnak, Compact isospectral sets of Riemannin surfaces, to appear in J. Funct. Anal.
  • [Sc] R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), no. 2, 479–495.
  • [Su] T. Sunada, Riemannian coverings and isospectral manifolds, Ann. of Math. (2) 121 (1985), no. 1, 169–186.
  • [Tr] N. S. Trudinger, Remarks concerning the conformal deformation of Riemannian structures on compact manifolds, Ann. Scuola Norm. Sup. Pisa (3) 22 (1968), 265–274.