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 $\R^n$ 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.
- Publication:
-
Inventiones Mathematicae
- Pub Date:
- August 2001
- DOI:
- 10.1007/s002220100150
- arXiv:
- arXiv:math/0005156
- Bibcode:
- 2001InMat.145..317G
- Keywords:
-
- Mathematics - Differential Geometry;
- 58G25;
- 53C20
- E-Print:
- 16 pages