English

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.

Keywords

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

R2 v1 2026-06-22T17:45:07.799Z