Anosov representations with Lipschitz limit set

Pozzetti, Maria Beatrice¹ ; Sambarino, Andrés² ; Wienhard, Anna³

¹ Mathematical Institute, Heidelberg University, Heidelberg, Germany
² IMJ-PRG, Sorbonne Université, CNRS, Paris, France
³ Mathematisches Institut, Universität Heidelberg, Heidelberg, Germany

Geometry & topology, Tome 27 (2023) no. 8, pp. 3303-3360.

Résumé

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 $\Theta$–positive representations, belong to this class, and establish several applications to rigidity results on the orbit growth rate in the symmetric space.

Détail

DOI : 10.2140/gt.2023.27.3303

Keywords: Anosov representations, Patterson–Sullivan measures

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