Hausdorff dimensions of limit sets. I

DOI10.1007/BF01233439zbMath0744.53030MaRDI QIDQ1173882

Kevin Corlette

Publication date: 25 June 1992

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143845

zbMATH Keywords

Hausdorff dimensionlimit setsRiemannian symmetric spacediscrete groups of isometriescocompact groups

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Differential geometry of symmetric spaces (53C35)

Related Items (44)

Riesz means on locally symmetric spaces ⋮ A note on complex-hyperbolic Kleinian groups ⋮ On conformal qc geometry, spherical qc manifolds and convex cocompact subgroups of \(\mathrm{Sp}{(n+1,1)}\) ⋮ Patterson–Sullivan theory for Anosov subgroups ⋮ The \(L^p\) spectrum of locally symmetric spaces with small fundamental group ⋮ On 𝐿² cohomology of ACH Kähler manifolds ⋮ A Survey of Complex Hyperbolic Kleinian Groups ⋮ New time-changes of unipotent flows on quotients of Lorentz groups ⋮ Counting and equidistribution in quaternionic Heisenberg groups ⋮ Unnamed Item ⋮ Wave and Klein-Gordon equations on certain locally symmetric spaces ⋮ The quasi-isometry classification of rank one lattices ⋮ Geometric estimates on weighted p-fundamental tone and applications to the first eigenvalue of submanifolds with bounded mean curvature ⋮ Hausdorff dimension and Kleinian groups ⋮ Hausdorff dimension of limit sets ⋮ Critical exponents of invariant random subgroups in negative curvature ⋮ Critical exponents of normal subgroups, the spectrum of group extended transfer operators, and Kazhdan distance ⋮ Poincaré series for non-Riemannian locally symmetric spaces ⋮ STRUCTURAL STABILITY OF MEANDERING-HYPERBOLIC GROUP ACTIONS ⋮ Hausdorff dimension of directional limit sets for self-joinings of hyperbolic manifolds ⋮ Canonical contact forms on spherical CR manifolds ⋮ Some asymptotic properties of random walks on homogeneous spaces ⋮ An inner product formula on two-dimensional complex hyperbolic space ⋮ HEAT KERNEL BOUNDS, POINCARÉ SERIES, AND L² SPECTRUM FOR LOCALLY SYMMETRIC SPACES ⋮ The ergodic theory of discrete isometry groups on manifolds of variable negative curvature ⋮ Resolvent of the Laplacian on strictly pseudoconvex domains ⋮ The spectrum of Kleinian manifolds ⋮ LERF and the Lubotzky-Sarnak conjecture ⋮ Asymptotic properties of coverings in negative curvature ⋮ Small eigenvalues of geometrically finite manifolds ⋮ Ergodicity of generalised Patterson-Sullivan measures in higher rank symmetric spaces ⋮ Growth gap in hyperbolic groups and amenability ⋮ Geometric invariants of locally symmetric spaces and multiplier theorems ⋮ Critical exponents of discrete groups and 𝐿²–spectrum ⋮ The Yamabe operator and invariants on octonionic contact manifolds and convex cocompact subgroups of \(F_{4(-20)}\) ⋮ Spectral estimates and discreteness of spectra under Riemannian submersions ⋮ Bottom of the \(L^2\) spectrum of the Laplacian on locally symmetric spaces ⋮ A vanishing theorem for the homology of discrete subgroups of Sp( n , 1) and F ₄ ^–20 ⋮ Growth of quasiconvex subgroups ⋮ Gradient estimate for harmonic functions on Kähler manifolds ⋮ Cheeger constants and \(L^2\)-Betti numbers ⋮ Limit sets of discrete groups of isometries of exotic hyperbolic spaces ⋮ An approach to symmetric spaces of rank one via groups of Heisenberg type ⋮ Deformation of Schottky groups in complex hyperbolic space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Carnot-Caratheodory metrics
• The Dirichlet problem at infinity for manifolds of negative curvature
• Analysis of the Laplacian on a complete Riemannian manifold
• Analysis on nilpotent groups
• Sub-Riemannian geometry
• The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• The density at infinity of a discrete group of hyperbolic motions
• Resolvent of the Laplacian on strictly pseudoconvex domains
• The limit set of a Fuchsian group
• Spherical hypersurfaces in complex manifolds
• On the principle of uniformization
• Related aspects of positivity in Riemannian geometry
• Die Resolvente von Delta auf symmetrischen Räumen vom nichtkompakten Typ
• Visibility manifolds
• On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold
• Conformal geometry in higher dimensions. I
• On the existence and irreducibility of certain series of representations

This page was built for publication: Hausdorff dimensions of limit sets. I