Basmajian-type inequalities for maximal representations

TL;DR

This paper generalizes Basmajian's identity to maximal representations of surface groups, establishing inequalities relating boundary lengths and orthogeodesic lengths in associated symmetric spaces, with equality characterizing diagonal embeddings.

Contribution

It introduces new inequalities for maximal representations that extend classical Teichmüller theory results to higher rank symmetric spaces.

Findings

Established inequalities between boundary and orthogeodesic lengths

Characterized cases of equality as diagonal embeddings

Extended Basmajian's identity to a broader geometric setting

Abstract

For suitable metrics on the locally symmetric space associated to a maximal representation, we prove inequalities between the length of the boundary and the lengths of orthogeodesics that generalize the classical Basmajian's identity from Teichmueller theory. Any equality characterizes diagonal embeddings.