Fabio Cavalletti

Self-intersection of optimal geodesics

Let

The Monge Problem in Geodesic Spaces

(X,d,m)

The polar cone of the set of monotone maps

be a geodesic metric measure space. Consider a geodesic

Optimal Transport with Branching Distance Costs and the Obstacle Problem

\mu_{t}

The Monge Problem for Distance Cost in Geodesic Spaces

in the

Local curvature-dimension condition implies measure-contraction property

L^{2}

Decomposition of Geodesics in the Wasserstein Space and the Globalization Problem

-Wasserstein space. Then as

MONGE PROBLEM IN METRIC MEASURE SPACES WITH RIEMANNIAN CURVATURE-DIMENSION CONDITION

s

Existence and uniqueness of optimal transport maps

goes to

The Monge problem in Wiener space

t