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.
Farre, J., Pozzetti, B., Viaggi, G. (In stampa/Attività in corso). Topological and geometric restrictions on hyperconvex representations. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, Ahead of pubblication, --- [10.1515/crelle-2025-0047].
Topological and geometric restrictions on hyperconvex representations
Beatrice Pozzetti;
In corso di stampa
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.File in questo prodotto:
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