Isospectral deformations of metrics on spheres

Details Isospectral deformations of metrics on spheres Isospectral deformations of metrics on spheres

2000-05-16

arxiv.org/abs/math/0005156v2

Mathematics

Differential Geometry

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

Scientific paper

10.1007/s002220100150

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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