Equivariant inverse spectral theory and toric orbifolds
Name
Guillemin_Equivariant inverse spectral.pdf
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269.54 KB
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Author(s)
Dryden, Emily B.
Sena-Dias, Rosa Isabel
Guillemin, Victor W.
Date Issued
August 2012
Journal
Advances in Mathematics
Publisher
Elsevier
Citation
Dryden, Emily B., Victor Guillemin, and Rosa Sena-Dias. “Equivariant inverse spectral theory and toric orbifolds.” Advances in Mathematics 231, no. 3 4 (October 2012): 1271-1290.
Version
Original manuscript
Abstract
Let O[superscript 2n] be a symplectic toric orbifold with a fixed T[superscript n]-action and with a toric Kähler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace operator Δ[subscript g] on C[superscript ∞](O) determines O up to symplectomorphism. In the setting of toric orbifolds we significantly improve upon our previous results and show that a generic toric orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kähler metric has constant scalar curvature.
Description
Original manuscript July 5, 2011
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1016/j.aim.2012.06.018
