Hitchin representations of Fuchsian groups

DOI10.4171/emss/61arXiv2110.01043OpenAlexW3204640096MaRDI QIDQ6150000

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Publication date: 6 February 2024

Published in: EMS Surveys in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.01043

zbMATH Keywords

entropyaugmented Teichmüller spaceHitchin representationspositive representations

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) General geometric structures on low-dimensional manifolds (57M50) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Teichmüller theory; moduli spaces of holomorphic dynamical systems (37F34) Fuchsian and Kleinian groups as dynamical systems (37F32)

Cites Work

• Pressure metrics for deformation spaces of quasifuchsian groups with parabolics
• McShane Identities for Higher Teichmüller Theory and the Goncharov–Shen Potential
• Hessian of Hausdorff dimension on purely imaginary directions
• Invariant Measures for Horospherical Actions and Anosov Groups
• Geodesic coordinates for the pressure metric at the Fuchsian locus
• Hitchin components for orbifolds
• The Hopf-Tsuji-Sullivan dichotomy in higher rank and applications to Anosov subgroups
• Horospherical invariant measures and a rank dichotomy for Anosov groups
• Correlation of the renormalized Hilbert length for convex projective surfaces
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• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Teichmüller space is totally geodesic in Goldman space
• Finite volume convex projective surface
• Compactifications of representation spaces of finitely generated groups
• Parameterizing Hitchin components
• The pressure metric for Anosov representations
• A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory
• Cyclic surfaces and Hitchin components in rank 2
• Anosov representations and proper actions
• Patterson-Sullivan measures in higher rank
• Marked moduli space of finite-volume convex projective surfaces
• Simple root flows for Hitchin representations
• Deforming convex real projective structures
• On the Hilbert geometry of simplicial Tits sets
• Flows on the PGL(V)-Hitchin component
• Cross ratios and identities for higher Teichmüller-Thurston theory
• Degeneration of Hitchin representations along internal sequences
• Renewal theorems in symbolic dynamics, with applications to geodesic flows, noneuclidean tessellations and their fractal limits
• Convex real projective structures on compact surfaces
• Cross ratios, surface groups, \(\text{PSL}(n,\mathbb R)\) and diffeomorphisms of the circle
• Flat projective structures on surfaces and cubic holomorphic differentials
• Thermodynamics, dimension and the Weil-Petersson metric
• Fluctuations of ergodic sums for horocycle flows on \(\mathbb Z^d\)-covers of finite volume surfaces
• Hausdorff dimension and the Weil-Petersson extension to quasifuchsian space
• Hitchin components and hyperconvex representations of surface groups
• Three-dimensional Anosov flag manifolds
• Lifting representations to covering groups
• Thurston's Riemannian metric for Teichmüller space
• The geometry of Teichmüller space via geodesic currents
• Hausdorff dimension of quasi-circles
• Markov maps associated with Fuchsian groups
• The real analytic theory of Teichmüller space
• Lie groups and Teichmüller space
• Infinitesimal conjugacies and Weil-Petersson metric
• Degenerating families of Riemann surfaces
• The extension of the Weil-Petersson metric to the boundary of Teichmüller space
• The parametrisation of the Teichmüller space by geodesic length functions
• Hausdorff dimension and Kleinian groups
• Positivity and higher Teichmüller theory
• Hitchin characters and geodesic laminations
• Anosov subgroups: dynamical and geometric characterizations
• Representation theoretic rigidity in \(PSL(2,\mathbb{R})\)
• The correlation of length spectra of two hyperbolic surfaces
• Volume growth, entropy and the geodesic stretch
• Anosov representations: domains of discontinuity and applications.
• Anosov representations and dominated splittings
• Conformality for a robust class of non-conformal attractors
• The real spectrum compactification of character varieties: characterizations and applications
• Narrow equidistribution and counting of closed geodesics on noncompact manifolds
• Counting, equidistribution and entropy gaps at infinity with applications to cusped Hitchin representations
• Relatively dominated representations
• Non-uniqueness of minimal surfaces in a product of closed Riemann surfaces
• Eigenvalue gaps for hyperbolic groups and semigroups
• Pressure metrics and Manhattan curves for Teichmüller spaces of punctured surfaces
• Simple length rigidity for Hitchin representations
• Convex \(\mathbb{RP}^2\) structures and cubic differentials under neck separation
• Collar lemma for Hitchin representations
• Kähler metric on the space of convex real projective structures on surface
• Volume entropy of Hilbert metrics and length spectrum of Hitchin representations into \(\mathrm{PSL}(3,\mathbb{R})\)
• Maximal representations, non-Archimedean Siegel spaces, and buildings
• Eigenvalues and entropy of a Hitchin representation
• Positively ratioed representations
• Moduli spaces of local systems and higher Teichmüller theory
• Anosov flows, surface groups and curves in projective space
• Quantitative properties of convex representations
• Counting problems for special-orthogonal Anosov representations
• Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups
• Relatively dominated representations from eigenvalue gaps and limit maps
• Affine spheres and convex [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /-manifolds]
• Entropy degeneration of convex projective surfaces
• Length asymptotics in higher Teichmüller theory
• The curious moduli spaces of unmarked Kleinian surface group
• Uniformization of surface laminations
• An introduction to pressure metrics for higher Teichmüller spaces
• A collar lemma for partially hyperconvex surface group representations
• The degeneration of convex ℝℙ²structures on surfaces
• The classification of real projective structures on compact surfaces
• Some negatively curved manifolds with cusps, mixing and counting
• Variations along the Fuchsian locus
• The return sequence of the Bowen–Series map for punctured surfaces
• Splittings of Surfaces
• Thermodynamic formalism for countable Markov shifts
• Regularity of entropy, geodesic currents and entropy at infinity
• Higher Teichmüller Theory for Surface Groups and Shifts of Finite Type
• Higher Complex Structures
• Coordinates on the augmented moduli space of convex RP2 structures
• Currents, systoles, and compactifications of character varieties
• Hyperconvex representations and exponential growth
• Basmajian's identity in higher Teichmüller–Thurston theory
• Cross ratios, Anosov representations and the energy functional on Teichmüller space
• The deformation spaces of convex RP 2 -structures on 2-orbifolds
• Growth of Quadratic Forms Under Anosov Subgroups
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• The orbital counting problem for hyperconvex representations
• Anosov groups: local mixing, counting and equidistribution

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