Marked length rigidity for symmetric spaces
The authors prove a marked-length-spectrum rigidity result for Zariski dense subgroups \(\Gamma\) of a connected semisimple Lie group \(G\) without compact factor and with trivial center. Namely, every surjective homomorphism \(\varphi:\Gamma\to\Gamma'\) between two such subgroups of \(G\), \(G'\) which preserves the translation lengths extends to a continuous isomorphism of \(G\) onto \(G'\). The proof is a remarkably simple application of a result of \textit{Y. Benoist} [Geom. Funct. Anal. 7, 1-47 (1997; Zbl 0947.22003)] on limit cones of Zariski dense subgroups of simple Lie groups of noncompact type.
scientific article; zbMATH DE number 1807867