Minimal entropy rigidity for Finsler manifolds of negative flag curvature

We define a normalized entropy functional for compact Finsler manifolds of negative flag curvature. Using the method of Besson, Courtois, and Gallot, we show that among all such manifolds that are homotopy equivalent to a com pact, Riemannian, locally symmetric manifold of negative curvature, the ent ropy functional is minimized precisely on the locally symmetric manifold.