Basmajian-type inequalities for maximal representations

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.

arXiv comment46 pages, 8 figures. Main addition: collar lemma-type statement for the locally symmetric space associated to a maximal representation. Further corrections/clarifications following referees' comments