Duke Mathematical Journal

Isospectral sets of conformally equivalent metrics

Robert Brooks, Peter Perry, and Paul Yang

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Article information

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

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077307376

Digital Object Identifier
doi:10.1215/S0012-7094-89-05808-0

Mathematical Reviews number (MathSciNet)
MR1016417

Zentralblatt MATH identifier
0667.53037

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

Citation

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.


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References

  • [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.