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

Autor:	Dryden, Emily B., Macedo, Diana, Sena-Dias, Rosa
Rok vydání:	2015
Předmět:	Mathematics - Spectral Theory Primary 58J50 Secondary 81Q20 53D20
Druh dokumentu:	Working Paper
Popis:	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. Comment: 16 pages; minor revisions throughout following comments from referees
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1501.02830 Zobrazit plný text záznamu View this record from Arxiv