Strong spectral gaps for compact quotients of products of $\mathrm{PSL}(2,\mathbb{R})$

Proof-critical source

Bounded trajectories of quasi-rays

This paper is included only for the following marked statements:

• Rank-one spectral-gap branch · journal p. 285; author PDF p. 3Uses discreteness of the Laplace spectrum below the continuous spectrum in the simple rank-one case.
• Property-(T) spectral-gap branch · journal p. 285; author PDF p. 3Combines property (T) with a finite group-dependent matrix-coefficient integrability exponent when the simple group has real rank at least two.
• Arithmetic product-lattice spectral-gap branch · journal pp. 284–285; author PDF pp. 2–3Combines arithmeticity, congruence spectral gap, automorphic transfer, and finite-cover invariance for irreducible lattices in products.