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Topological and geometric restrictions on hyperconvex representations

  • James Farre EMAIL logo , Beatrice Pozzetti and Gabriele Viaggi ORCID logo
Published/Copyright: July 30, 2025

Abstract

We study the geometry of hyperconvex representations of hyperbolic groups in PSL ( d , C ) and establish two structural results: a group admitting a hyperconvex representation is virtually isomorphic to a Kleinian group, and its hyperconvex limit set in the appropriate flag manifold has Hausdorff dimension strictly smaller than 2.

Award Identifier / Grant number: 427903332

Award Identifier / Grant number: EXC-2181/1-390900948

Award Identifier / Grant number: 281071066

Funding statement: This work was funded through the DFG Emmy Noether project 427903332 of Beatrice Pozzetti. Beatrice Pozzetti acknowledges additional support by the DFG under Germany’s Excellence Strategy EXC-2181/1-390900948. James Farre acknowledges support from DFG – Project-ID 281071066 – TRR 191.

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Received: 2024-06-14
Revised: 2025-06-24
Published Online: 2025-07-30
Published in Print: 2025-10-01

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