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Anosov representations
with Lipschitz limit set
Maria Beatrice Pozzetti, Andrés Sambarino and Anna Wienhard |
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Geometry & Topology 27 (2023) 3303–3360
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Abstract |
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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 –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
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Mathematical Subject Classification
Primary: 22E40, 51F30
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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
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Authors |
| Maria Beatrice Pozzetti | |
| Mathematical Institute Heidelberg University Heidelberg Germany |
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| Andrés Sambarino | |
| IMJ-PRG Sorbonne Université, CNRS Paris France |
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| Anna Wienhard | |
| Mathematisches Institut Universität Heidelberg Heidelberg Germany |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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