An intrinsic parallel transport in Wasserstein space
Differential Geometry
2017-01-10 v1
Abstract
If M is a smooth compact connected Riemannian manifold, let P(M) denote the Wasserstein space of probability measures on M. We describe a geometric construction of parallel transport of some tangent cones along geodesics in P(M). We show that when everything is smooth, the geometric parallel transport agrees with earlier formal calculations.
Cite
@article{arxiv.1701.02297,
title = {An intrinsic parallel transport in Wasserstein space},
author = {John Lott},
journal= {arXiv preprint arXiv:1701.02297},
year = {2017}
}
Comments
final version, 13 pages, split off from an earlier version of arXiv:1407.7245