{"paper":{"title":"Recovering $S^1$-invariant metrics on $S^2$ from the equivariant spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Diana Macedo, Emily B. Dryden, Rosa Sena-Dias","submitted_at":"2015-01-12T21:23:17Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02830","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}