Marked length rigidity for symmetric spaces

Abstract.

We give conditions under which a homomorphism between two Zariski dense subgroups of connected semisimple Lie groups G and G' without compact factors and with trivial center can be extended to a continuous isomorphism between G and G'. In particular we prove the marked length rigidity and the marked translation vector rigidity. This last result was motivated by a Margulis‚s question.