Abstract
In this paper we investigate the Hausdorff dimension of limit sets of Anosov representations. In this context we revisit and extend the framework of hyperconvex representations and establish a convergence property for them, analogue to a differentiability property. As an application of this convergence, we prove that the Hausdorff dimension of the limit set of a hyperconvex representation is equal to a suitably chosen critical exponent.
Funding source: Agence Nationale de la Recherche
Award Identifier / Grant number: ANR-16-CE40-0025
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: 338644254
Funding source: European Research Council
Award Identifier / Grant number: 614733
Funding statement: Andrés Sambarino was partially financed by ANR DynGeo ANR-16-CE40-0025. Beatrice Pozzetti and Anna Wienhard acknowledge funding by the Deutsche Forschungsgemeinschaft Project number 338644254 within the Priority Program SPP 2026 “Geometry at Infinity”. Anna Wienhard acknowledges funding by the European Research Council under ERC-Consolidator grant 614733, and by the Klaus-Tschira-Foundation.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Conformality for a robust class of non-conformal attractors
- Characteristic cycles and the microlocal geometry of the Gauss map, II
- The resolution property via Azumaya algebras
- Base change for ramified unitary groups: The strongly ramified case
- Fano manifolds and stability of tangent bundles
- Positive solutions to Schrödinger equations and geometric applications
- Lagrangian cobordism and tropical curves
- The fundamental group, rational connectedness and the positivity of Kähler manifolds
Artikel in diesem Heft
- Frontmatter
- Conformality for a robust class of non-conformal attractors
- Characteristic cycles and the microlocal geometry of the Gauss map, II
- The resolution property via Azumaya algebras
- Base change for ramified unitary groups: The strongly ramified case
- Fano manifolds and stability of tangent bundles
- Positive solutions to Schrödinger equations and geometric applications
- Lagrangian cobordism and tropical curves
- The fundamental group, rational connectedness and the positivity of Kähler manifolds