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Inventiones mathematicae

, Volume 145, Issue 2, pp 317–331 | Cite as

Isospectral deformations of metrics on spheres

  • Carolyn S. Gordon

Abstract.

We construct non-trivial continuous isospectral deformations of Riemannian metrics on the ball and on the sphere in R n for every n≥9. The metrics on the sphere can be chosen arbitrarily close to the round metric; in particular, they can be chosen to be positively curved. The metrics on the ball are both Dirichlet and Neumann isospectral and can be chosen arbitrarily close to the flat metric.

Mathematics Subject Classification (1991): 58G25, 53C20, 22E25 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Carolyn S. Gordon
    • 1
  1. 1.Dartmouth College, Hanover, New Hampshire, 03755, USA (e-mail: carolyn.s.gordon@dartmouth.edu)US

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