An intrinsic parallel transport in Wasserstein space

John Lott

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arXiv · 1701.02297

An intrinsic parallel transport in Wasserstein space

John Lott

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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.

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John Lott. 2017-01-09. An intrinsic parallel transport in Wasserstein space. https://arxiv.org/abs/1701.02297

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