Recovering $S^1$-Invariant Metrics on $S^2$ from the Equivariant Spectrum

Authors

Emily Dryden, Bucknell UniversityFollow
Rosa Sena-Dias, Instituto Superior TecnicoFollow
Diana Macedo, Instituto Superior Tecnico

Publication Date

2016

Description

We prove an inverse spectral result for S1-invariant metrics on S² based on the so-called asymptotic equivariant spectrum. This is roughly the spectrum together with large weights of the S¹-action on the eigenspaces. Our result generalizes an inverse spectral result from [6] concerning S¹-invariant metrics on S² which are invariant under the antipodal map. We use higher order terms in the asymptotic expansion of a natural spectral measure associated with the Laplacian and the S¹-action.

Journal

International Mathematics Research Notices

Volume

16

First Page

4882

Last Page

4902

Department

Mathematics

Recommended Citation

Dryden, Emily; Sena-Dias, Rosa; and Macedo, Diana. "Recovering $S^1$-Invariant Metrics on $S^2$ from the Equivariant Spectrum." International Mathematics Research Notices (2016) : 4882-4902.