Some geometric calculations on Wasserstein space
John Lott
TL;DR
This paper computes the Riemannian connection and curvature of the Wasserstein space over a smooth compact Riemannian manifold, providing geometric insights into its structure.
Contribution
It introduces explicit calculations of geometric quantities like connection and curvature for Wasserstein space on smooth manifolds, advancing understanding of its geometric properties.
Findings
Explicit formulas for Riemannian connection
Curvature computations for Wasserstein space
Enhanced geometric understanding of Wasserstein space
Abstract
We compute the Riemannian connection and curvature for the Wasserstein space of a smooth compact Riemannian manifold.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Neuroimaging Techniques and Applications