Volume entropy of Hilbert metrics and length spectrum of Hitchin representations into \(\mathrm{PSL}(3,\mathbb{R})\)

DOI10.1215/00127094-00000010XzbMath1375.53022arXiv1506.04640OpenAlexW3098209288MaRDI QIDQ2359432

Publication date: 28 June 2017

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.04640

zbMATH Keywords

Blaschke metric Hilbert geometry volume entropy Hilbert metric Hitchin representation surface group representation

Mathematics Subject Classification ID

Length, area, volume and convex sets (aspects of convex geometry) (52A38) General geometric structures on low-dimensional manifolds (57M50) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Projective differential geometry (53A20) Affine differential geometry (53A15)

Related Items (16)

Dominating surface-group representations into \(\mathrm{PSL}_2 (\mathbb{C})\) in the relative representation variety ⋮ Conjectures on Reductive Homogeneous Spaces ⋮ On the entropy of Hilbert geometries of low regularities ⋮ McShane Identities for Higher Teichmüller Theory and the Goncharov–Shen Potential ⋮ The covariance metric in the Blaschke locus ⋮ Hitchin representations of Fuchsian groups ⋮ Correlation of the renormalized Hilbert length for convex projective surfaces ⋮ Convex geometry and its applications. Abstracts from the workshop held December 12--18, 2021 (hybrid meeting) ⋮ Entropy rigidity for finite volume strictly convex projective manifolds ⋮ Entropy rigidity and Hilbert volume ⋮ Optimal inequalities between distances in convex projective domains ⋮ Simple root flows for Hitchin representations ⋮ Ergodicity of Bowen-Margulis measure for the Benoist 3-manifolds ⋮ The geometry of maximal representations of surface groups into \(\mathrm{SO}_0(2,n)\) ⋮ Proof of Kobayashi's rank conjecture on Clifford-Klein forms ⋮ Projective Anosov representations, convex cocompact actions, and rigidity

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