Recovering $S^1$-invariant metrics on $S^2$ from the equivariant spectrum

Emily B. Dryden; Diana Macedo; Rosa Sena-Dias

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arXiv · 1501.02830

Recovering $S^1$-invariant metrics on $S^2$ from the equivariant spectrum

Emily B. Dryden·Diana Macedo·Rosa Sena-Dias

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Abstract

We prove an inverse spectral result for $S^1$-invariant metrics on $S^2$ based on the so-called asymptotic equivariant spectrum. This is roughly the spectrum together with large weights of the $S^1$ action on the eigenspaces. Our result generalizes an inverse spectral result of the first and last named authors, together with Victor Guillemin, concerning $S^1$-invariant metrics on $S^2$ 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 $S^1$ action.

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BibTeX RIS

Emily B. Dryden, Diana Macedo, Rosa Sena-Dias. 2015-01-12. Recovering $S^1$-invariant metrics on $S^2$ from the equivariant spectrum. https://arxiv.org/abs/1501.02830

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