Isospectral deformations of metrics on spheres

Abstract

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

16 pages; correction in introduction: to author's knowledge, there are no other known examples of continuous isospectral deformations of metrics on spheres

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