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Anosov representations with Lipschitz limit set

Maria Beatrice Pozzetti, Andrés Sambarino and Anna Wienhard

Geometry & Topology 27 (2023) 3303–3360
Abstract

We study Anosov representations whose limit set has intermediate regularity, namely is a Lipschitz submanifold of a flag manifold. We introduce an explicit linear functional, the unstable Jacobian, whose orbit growth rate is integral on this class of representations. We prove that many interesting higher-rank representations, including Θ–positive representations, belong to this class, and establish several applications to rigidity results on the orbit growth rate in the symmetric space.

Keywords
Anosov representations, Patterson–Sullivan measures
Mathematical Subject Classification
Primary: 22E40, 51F30
References
Publication
Received: 25 June 2021
Revised: 31 December 2021
Accepted: 5 February 2022
Published: 9 November 2023
Proposed: David Fisher
Seconded: Mladen Bestvina, Ian Agol
Authors
Maria Beatrice Pozzetti
Mathematical Institute
Heidelberg University
Heidelberg
Germany
Andrés Sambarino
IMJ-PRG
Sorbonne Université, CNRS
Paris
France
Anna Wienhard
Mathematisches Institut
Universität Heidelberg
Heidelberg
Germany

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