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. (2025). Topological and geometric restrictions on hyperconvex representations. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 827, 227-251 [10.1515/crelle-2025-0047].
Topological and geometric restrictions on hyperconvex representations
Beatrice Pozzetti;
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.File in questo prodotto:
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Higher_Kleinian_Groups_2_0 (1).pdf
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