Medians and means in Finsler geometry

We investigate existence and uniqueness of p-means ep and the median e1 of a probability measure μ on a Finsler manifold, in relation with the convexity of the support of μ. We prove that ep 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 ep. This provides an algorithm for determining the Finsler center points.