Medians and means in Finsler 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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2010
- DOI:
- arXiv:
- arXiv:1011.6076
- Bibcode:
- 2010arXiv1011.6076A
- Keywords:
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- Mathematics - Differential Geometry;
- Computer Science - Computational Geometry
- E-Print:
- LMS J. Comput. Math. 15 (2012) 23-37