Anosov representations with Lipschitz limit set

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

arXiv commentseveral changes in the introduction, minor corrections elsewhere

References in corpus (10)

• A Morse Lemma for quasigeodesics in symmetric spaces and euclidean buildings
• Anosov representations and dominated splittings
• Topological Invariants of Anosov Representations
• Morse actions of discrete groups on symmetric space
• Deformations of maximal representations in Sp(4,R)
• Hyperconvex representations and exponential growth
• The geometry of maximal representations of surface groups into SO(2,n)
• Patterson-Sullivan theory for Anosov subgroups
• Proper affine actions for right-angled Coxeter groups
• Classification of tight homomorphisms

Cited by in corpus (4)

• Positive surface group representations in PO(p,q)
• Degenerations of k-positive surface group representations
• Uniformization of compact complex manifolds by Anosov representations
• Dimension gap and variational principle for Anosov representations