%0 Journal Article %1 arnaudon2010medians %A Arnaudon, Marc %A Nielsen, Frank %D 2010 %K geometry information %R 10.1112/S1461157010000513 %T Medians and means in Finsler geometry %U http://arxiv.org/abs/1011.6076 %X 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.

@article{arnaudon2010medians, 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.}, added-at = {2019-12-11T14:48:08.000+0100}, author = {Arnaudon, Marc and Nielsen, Frank}, biburl = {https://www.bibsonomy.org/bibtex/21c1f8d794e07e80a7ed72209c83d289c/kirk86}, description = {[1011.6076] Medians and means in Finsler geometry}, doi = {10.1112/S1461157010000513}, interhash = {b91c63a65e6f6acb2d82874684fc86f5}, intrahash = {1c1f8d794e07e80a7ed72209c83d289c}, keywords = {geometry information}, note = {cite arxiv:1011.6076}, timestamp = {2019-12-11T14:48:08.000+0100}, title = {Medians and means in Finsler geometry}, url = {http://arxiv.org/abs/1011.6076}, year = 2010 }