{"paper":{"title":"On entropy, regularity and rigidity for convex representations of hyperbolic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.DS"],"primary_cat":"math.GR","authors_text":"Andr\\'es Sambarino","submitted_at":"2013-03-27T14:45:19Z","abstract_excerpt":"Given a convex representation $\\rho:\\Gamma\\to\\textrm{PGL}(d,\\mathbb{R})$ of a convex co-compact group $\\Gamma$ of $\\mathbb{H}^k$ we find upper bounds for the quantity $\\alpha h_\\rho,$ where $h_\\rho$ is the entropy of $\\rho$ and $\\alpha$ is the H\\\"older exponent of the equivariant map $\\partial\\Gamma\\to\\mathbb{P}(\\mathbb{R}^d).$ We also give rigidity statements when the upper bound is attained. We then study Hitchin representations and prove that if $\\rho:\\pi_1\\Sigma\\to\\textrm{PSL}(d,\\mathbb{R})$ is in the Hitchin component then $\\alpha h_\\rho\\leq 2/(d-1)$ (where $\\alpha$ is the H\\\"older expone"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6846","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}