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15 October 2021 Spectral gap and exponential mixing on geometrically finite hyperbolic manifolds
Sam Edwards, Hee Oh
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Duke Math. J. 170(15): 3417-3458 (15 October 2021). DOI: 10.1215/00127094-2021-0051

Abstract

Let M=ΓHd+1 be a geometrically finite hyperbolic manifold with critical exponent exceeding d2. We obtain a precise asymptotic expansion of the matrix coefficients for the geodesic flow in L2(T1(M)), with exponential error term essentially as good as the one given by the spectral gap for the Laplace operator on L2(M) due to Lax and Phillips. Combined with the work of Bourgain, Gamburd, and Sarnak and its generalization by Golsefidy and Varjú on expanders, this implies uniform exponential mixing for congruence covers of M when Γ is a Zariski-dense subgroup contained in an arithmetic subgroup of SO(d,1).

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Sam Edwards. Hee Oh. "Spectral gap and exponential mixing on geometrically finite hyperbolic manifolds." Duke Math. J. 170 (15) 3417 - 3458, 15 October 2021. https://doi.org/10.1215/00127094-2021-0051

Information

Received: 13 January 2020; Revised: 23 November 2020; Published: 15 October 2021
First available in Project Euclid: 23 September 2021

Digital Object Identifier: 10.1215/00127094-2021-0051

Subjects:
Primary: 22E45

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 15 • 15 October 2021
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