Rigidity and quasisymmetric uniformization of Thurston-type maps

Abstract

We prove the No Invariant Line Fields conjecture for a class of generalized postcritically-finite branched covers on higher-dimensional Riemannian manifolds. Moreover, we establish a quasisymmetric uniformization theorem for this class of generalized postcritically-finite maps.

53 pages, 2 figures. The current version significantly generalized the previous version