Medians and means in Finsler geometry

We investigate existence and uniqueness of p -means e p and the median e 1 of a probability measure μ on a Finsler manifold, in relation with the convexity of the support of μ . We prove that e p is the limit point of a continuous time gradient flow. Under some additional condition which is always satisfied for p ≥2, a discretization of this path converges to e p . This provides an algorithm for determining the Finsler center points.