Hyperconvex representations and exponential growth

Abstract

Let $G$ be a real algebraic semi-simple Lie group and $\Gamma$ be the fundamental group of a compact negatively curved manifold. In this article we study the limit cone, introduced by Benoist, and the growth indicator function, introduced by Quint, for a class of representations $\rho :\Gamma \to G$ admitting a equivariant map from $\partial \Gamma$ to the Furstenberg boundary of $G$'s symmetric space together with a transversality condition. We then study how these objects vary with the representation.

References in corpus (1)

• Anosov representations: Domains of discontinuity and applications

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