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Isospectral deformations of metrics on spheres

Carolyn S. Gordon
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Abstract

We construct non-trivial continuous isospectral deformations of Riemannian metrics on the ball and on the sphere in $\R^n$ for every $n\geq 9$. 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.

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Carolyn S. Gordon. 2000-07-06. Isospectral deformations of metrics on spheres. https://doi.org/10.1007/s002220100150

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