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