Geodesic coordinates for the pressure metric at the Fuchsian locus

DOI10.2140/gt.2023.27.1391zbMath1522.53023arXiv1910.00792OpenAlexW2978600587WikidataQ122977907 ScholiaQ122977907MaRDI QIDQ6157236

Xian Dai

Publication date: 20 June 2023

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.00792

zbMATH Keywords

thermodynamic formalismHiggs bundleHitchin representationpressure metric

Mathematics Subject Classification ID

Geometric group theory (20F65) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Geodesics in global differential geometry (53C22) 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) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Related Items (2)

The covariance metric in the Blaschke locus ⋮ Hitchin representations of Fuchsian groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The pressure metric for Anosov representations
• Simple root flows for Hitchin representations
• Convex real projective structures on compact surfaces
• Thermodynamics, dimension and the Weil-Petersson metric
• On the rate of mixing of Axiom A flows
• The Teichmüller theory of harmonic maps
• Lie groups and Teichmüller space
• The ergodic theory of axiom A flows
• Noncompleteness of the Weil-Petersson metric for Teichmüller space
• Derivatives of topological entropy for Anosov and geodesic flows
• Geodesic length functions and the Nielsen problem
• The Weil-Petersson isometry group
• Simple length rigidity for Hitchin representations
• Eigenvalues and entropy of a Hitchin representation
• Anosov flows, surface groups and curves in projective space
• Quantitative properties of convex representations
• Some remarks on Teichmüller's space of Riemann surfaces
• Markov partitions for Anosov flows on \(n\)-dimensional manifolds
• The pressure and higher correlations for an Anosov diffeomorphism
• Survey on Affine Spheres
• The Self-Duality Equations on a Riemann Surface
• Constructing Variations of Hodge Structure Using Yang-Mills Theory and Applications to Uniformization
• Elliptic Partial Differential Equations of Second Order
• Variations along the Fuchsian locus
• Symbolic Dynamics for Hyperbolic Flows
• Convex Real Projective Structures on Closed Surfaces are Closed
• Markov Partitions for Axiom A Diffeomorphisms
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• The orbital counting problem for hyperconvex representations

This page was built for publication: Geodesic coordinates for the pressure metric at the Fuchsian locus