Kleinian Schottky groups, Patterson-Sullivan measures, and Fourier decay
DOI10.1215/00127094-2020-0058zbMath1475.30104arXiv1902.01103OpenAlexW3110811117MaRDI QIDQ2037844
Jialun Li, Frédéric Naud, Wenyu Pan
Publication date: 8 July 2021
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1902.01103
Fourier transformadditive combinatoricsSchottky groupsPatterson-Sullivan measuresHausdorff and Fourier dimension transfer operatorslimit sets of Kleininan groupsrandom walks on linear groups
Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Discrete subgroups of Lie groups (22E40) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40) Fuchsian and Kleinian groups as dynamical systems (37F32)
Related Items (10)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Fourier transforms of Gibbs measures for the Gauss map
- Spectral gaps, additive energy, and a fractal uncertainty principle
- The discretized sum-product and projection theorems
- Asymptotic properties of linear groups
- A spectral gap theorem in SU\((d)\)
- Homological dimension and critical exponent of Kleinian groups
- Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits
- Free groups in lattices
- Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
- Regenerative representation for one-dimensional Gibbs states
- On the bass note of a Schottky group
- On decay of correlations in Anosov flows
- The density at infinity of a discrete group of hyperbolic motions
- Decrease of Fourier coefficients of stationary measures
- Dolgopyat's method and the fractal uncertainty principle
- On uniform exponential growth for linear groups.
- Random recursive construction of Salem sets
- Cusp excursion in hyperbolic manifolds and singularity of harmonic measure
- Large degree covers and sharp resonances of hyperbolic surfaces
- Topological proof of Benoist-Quint's orbit closure theorem for \(\mathrm{SO}(d, 1) \)
- A Fatou theorem for conformal densities with applications to Galois coverings in negative curvature
- Explicit Salem sets in \(\mathbb{R}^2\)
- Fourier dimension and spectral gaps for hyperbolic surfaces
- Harmonicity of quasiconformal measures and Poisson boundaries of hyperbolic spaces
- On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\)
- A characterization of Schottky groups
- A Poisson formula for semi-simple Lie groups
- Random Walks on Reductive Groups
- Spectra of Ruelle transfer operators for Axiom A flows
- Produits de matrices aléatoires et applications aux propriétés géometriques des sous-groupes du groupe linéaire
- Diophantine extremality of the Patterson measure
- Equilibrium states in negative curvature
- Lyapunov indices of a product of random matrices
- On the theorem of Jarník and Besicovitch
- Decoupling and Near-optimal Restriction Estimates for Cantor Sets
- Isometric actions of Lie subgroups of the Moebius group
- Ergodicité et équidistribution en courbure négative
- Fourier Analysis and Hausdorff Dimension
- Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions
- Spectral theory of infinite-area hyperbolic surfaces
This page was built for publication: Kleinian Schottky groups, Patterson-Sullivan measures, and Fourier decay
