Spectral gap and exponential mixing on geometrically finite hyperbolic manifolds
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Publication:2059020
DOI10.1215/00127094-2021-0051OpenAlexW3201951283WikidataQ115517625 ScholiaQ115517625MaRDI QIDQ2059020
Publication date: 13 December 2021
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2001.03377
Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Discrete subgroups of Lie groups (22E40) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)
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Cites Work
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- Generalization of Selberg's \(\frac {3}{16} \) theorem and affine sieve
- Sector estimates for hyperbolic isometries
- Affine linear sieve, expanders, and sum-product
- The density at infinity of a discrete group of hyperbolic motions
- The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces
- Ramanujan duals. II
- The limit set of a Fuchsian group
- Density of integer points on affine homogeneous varieties
- Mixing, counting, and equidistribution in Lie groups
- Rigidity, unitary representations of semisimple groups, and fundamental groups of manifolds with rank one transformation group
- On the mixing property for hyperbolic systems
- On the spectral gap for infinite index ``congruence subgroups of SL\(_2(\mathbb{Z})\)
- Variational principle and Kleinian groups
- Effective equidistribution of \(S\)-integral points on symmetric varieties
- Expansion in perfect groups.
- Some consequences of Arthur's work on the spectrum and topology of hyperbolic varieties
- The expressions of the Harish-Chandra \(C\)-functions of semisimple Lie groups \(\text{Spin}(n,1)\), \(\text{SU}(n,1)\)
- Quantitative spectral gap for thin groups of hyperbolic isometries
- Matrix coefficients, counting and primes for orbits of geometrically finite groups
- Counting, mixing and equidistribution of horospheres in geometrically finite rank one locally symmetric manifolds
- Closed geodesics and holonomies for Kleinian manifolds
- Intertwining operators for semisimple groups
- Effective Bisector Estimate with Application to Apollonian Circle Packings
- Spectra of Ruelle transfer operators for Axiom A flows
- Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds
- The rate of mixing for geodesic and horocycle flows
- On irreducible representations of the Lorentz group of $n$-th order
- Ergodicité et équidistribution en courbure négative
- Exponential mixing of frame flows for convex cocompact hyperbolic manifolds
- On the Quasi-Simple Irreducible Representations of the Lorentz Groups
- Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of $\operatorname {SL}_2(\mathbb {Z})$
- Lie groups beyond an introduction