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Sarnak’s spectral gap question
We answer in the affirmative a question of Sarnak’s from 2007, confirming that the Patterson–Sullivan base eigenfunction is the unique square-integrable eigenfunction of the hyperbolic Laplacian invariant under the group of symmetries of the Apollonian packing. Thus the latter has a maximal spectral gap. We prove further restrictions on the spectrum of the Laplacian on a wide class of manifolds coming from Kleinian sphere packings.
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- Award ID(s):
- 1651563
- PAR ID:
- 10513732
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Journal d'Analyse Mathématique
- ISSN:
- 0021-7670,1565-8538
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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