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arXiv · 1011.6076

Medians and means in Finsler geometry

Marc Arnaudon·Frank Nielsen
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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.

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Marc Arnaudon, Frank Nielsen. 2010-11-28. Medians and means in Finsler geometry. https://doi.org/10.1112/s1461157010000513

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