Sarnak’s spectral gap question

Dubi Kelmer, Alex Kontorovich, Christopher Lutsko

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)171-179
Number of pages9
JournalJournal d'Analyse Mathematique
Issue number1
StatePublished - Dec 2023

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)


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