The pressure metric for Anosov representations

DOI10.1007/s00039-015-0333-8zbMath1360.37078arXiv1301.7459OpenAlexW1752357772WikidataQ126271230 ScholiaQ126271230MaRDI QIDQ496174

François Labourie, Andrés Sambarino, Richard D. Canary, Martin J. Bridgeman

Publication date: 21 September 2015

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.7459

zbMATH Keywords

Riemannian metricthermodynamic formalismAnosov representationsWeil-Peterson metric

Mathematics Subject Classification ID

Geometric group theory (20F65) Semisimple Lie groups and their representations (22E46) General geometric structures on low-dimensional manifolds (57M50) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Manifolds of metrics (especially Riemannian) (58D17)

Related Items (58)

Positivity and higher Teichmüller theory ⋮ Thermodynamic metrics on outer space ⋮ Patterson–Sullivan theory for Anosov subgroups ⋮ From Hyperbolic Dehn Filling to Surgeries in Representation Varieties ⋮ Rigidity for convex-cocompact actions on rank-one symmetric spaces ⋮ An introduction to pressure metrics for higher Teichmüller spaces ⋮ On entropy, regularity and rigidity for convex representations of hyperbolic manifolds ⋮ Eigenvalue gaps for hyperbolic groups and semigroups ⋮ Hausdorff dimension and complex hyperbolic Schottky groups: a simplification ⋮ Hyperbolic systems, zeta functions and other friends ⋮ Counting problems for special-orthogonal Anosov representations ⋮ Cataclysms for Anosov representations ⋮ Eigenvalues and entropy of a Hitchin representation ⋮ Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups ⋮ Margulis multiverse: Infinitesimal rigidity, pressure form and convexity ⋮ Anosov groups: local mixing, counting and equidistribution ⋮ Anosov representations with Lipschitz limit set ⋮ A report on an ergodic dichotomy ⋮ Pressure metrics for deformation spaces of quasifuchsian groups with parabolics ⋮ Working session: Higher rank Teichmüller theory. Abstracts from the working session held October 9--14, 2022 ⋮ Entropy and affine actions for surface groups ⋮ Zeta functions in higher Teichmüller theory ⋮ Hessian of Hausdorff dimension on purely imaginary directions ⋮ Pressure metrics for cusped Hitchin components ⋮ Hitchin representations of Fuchsian groups ⋮ Geodesic coordinates for the pressure metric at the Fuchsian locus ⋮ Hitchin components for orbifolds ⋮ Hausdorff dimension of directional limit sets for self-joinings of hyperbolic manifolds ⋮ Correlation of the renormalized Hilbert length for convex projective surfaces ⋮ Tent property of the growth indicator functions and applications ⋮ Rigidity of geometric structures ⋮ Pseudo-Kähler geometry of properly convex projective structures on the torus ⋮ Mini-workshop: (Anosov)\(^3\). Abstracts from the mini-workshop held December 5--11, 2021 (hybrid meeting) ⋮ Pappus Theorem, Schwartz Representations and Anosov Representations ⋮ Incompleteness of the pressure metric on the Teichmüller space of a bordered surface ⋮ Basmajian-type inequalities for maximal representations ⋮ Pressure metrics and Manhattan curves for Teichmüller spaces of punctured surfaces ⋮ Parameterizing Hitchin components ⋮ The pressure metric on the Margulis multiverse ⋮ Goldman algebra, opers and the swapping algebra ⋮ Cyclic surfaces and Hitchin components in rank 2 ⋮ Specification and towers in shift spaces ⋮ Simple root flows for Hitchin representations ⋮ Convex cocompactness in pseudo-Riemannian hyperbolic spaces ⋮ Pressure type metrics on spaces of metric graphs ⋮ Variations along the Fuchsian locus ⋮ Conformality for a robust class of non-conformal attractors ⋮ Simple length rigidity for Hitchin representations ⋮ Strong symbolic dynamics for geodesic flows on \(\operatorname{CAT}(-1)\) spaces and other metric Anosov flows ⋮ Riemannian metrics on the moduli space of GHMC anti-de Sitter structures ⋮ A Glimpse into Thurston’s Work ⋮ Quasi-Fuchsian Co-Minkowski Manifolds ⋮ Projective Anosov representations, convex cocompact actions, and rigidity ⋮ Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations ⋮ Higher Teichmüller Theory for Surface Groups and Shifts of Finite Type ⋮ Geodesic stretch, pressure metric and marked length spectrum rigidity ⋮ Relatively dominated representations ⋮ Collar lemma for Hitchin representations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Teichmüller space is totally geodesic in Goldman space
• Length functions of Hitchin representations
• Lectures on representations of surface groups
• Cyclic surfaces and Hitchin components in rank 2
• Asymptotic properties of linear groups
• Differentiability and analyticity of topological entropy for Anosov and geodesic flows
• The thermodynamic formalism for expanding maps
• Cross ratios, surface groups, \(\text{PSL}(n,\mathbb R)\) and diffeomorphisms of the circle
• An extension of the Weil-Petersson metric to quasi-Fuchsian space
• Flat projective structures on surfaces and cubic holomorphic differentials
• Thermodynamics, dimension and the Weil-Petersson metric
• Hausdorff dimension and the Weil-Petersson extension to quasifuchsian space
• Thurston's Riemannian metric for Teichmüller space
• The geometry of Teichmüller space via geodesic currents
• Hausdorff dimension of quasi-circles
• The density at infinity of a discrete group of hyperbolic motions
• Lie groups and Teichmüller space
• The ergodic theory of axiom A flows
• The limit set of a Fuchsian group
• A small simplification in hyperbolic groups
• Rigidity and deformation spaces of strictly convex real projective structures on compact manifolds
• Automorphisms of convex cones
• Formulas for the derivative and critical points of topological entropy for Anosov and geodesic flows
• Symbolic coding for the geodesic flow associated to a word hyperbolic group.
• Anosov representations: domains of discontinuity and applications.
• Flows and joins of metric spaces
• Maximal representations of surface groups: symplectic Anosov structures
• Anosov flows, surface groups and curves in projective space
• Quantitative properties of convex representations
• Déformations de connexions localement plates
• Ergodic theory and rigidity on the symmetric space of non-compact type
• Affine spheres and convex [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /-manifolds]
• Length asymptotics in higher Teichmüller theory
• A variation formula for the topological entropy of convex-cocompact manifolds
• DEFORMATIONS OF MAXIMAL REPRESENTATIONS IN Sp(4, R)
• Convexes divisibles III
• Varieties of representations of finitely generated groups
• Symbolic Dynamics for Smale Flows
• Limit sets of discrete groups of isometries of exotic hyperbolic spaces
• A criterion of conjugacy for Zariski dense subgroups
• Variations along the Fuchsian locus
• Repellers for real analytic maps
• Symbolic Dynamics for Hyperbolic Flows
• The marked length spectrum of a projective manifold or orbifold
• Topological invariants of Anosov representations
• Hyperconvex representations and exponential growth
• COHOMOLOGY OF DYNAMICAL SYSTEMS
• Cross ratios, Anosov representations and the energy functional on Teichmüller space
• Shorter Notes: A Normal Subgroup of a Semisimple Lie Group is Closed
• Periodic Orbits for Hyperbolic Flows
• The ergodic theory of discrete isometry groups on manifolds of variable negative curvature
• Invariant manifolds
• Hyperbolic manifolds and discrete groups

This page was built for publication: The pressure metric for Anosov representations