Title

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

Publication Date

2016

Journal

International Mathematics Research Notices

Volume

16

First Page

4882

Last Page

4902

Department

Mathematics

Abstract

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.

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