Medians and means in Finsler geometry
Differential Geometry
2019-02-20 v2 Computational Geometry
Abstract
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.
Cite
@article{arxiv.1011.6076,
title = {Medians and means in Finsler geometry},
author = {Marc Arnaudon and Frank Nielsen},
journal= {arXiv preprint arXiv:1011.6076},
year = {2019}
}