A geometric study of Wasserstein spaces: an addendum on the boundary

TL;DR

This paper explores the geometric properties of Wasserstein spaces over negatively curved spaces, specifically trees, focusing on boundary point connections via geodesics.

Contribution

It extends previous geometric analyses of Wasserstein spaces by characterizing boundary point linkages in the context of trees.

Findings

Identifies which boundary points in Wasserstein space are connected by geodesics.

Provides new insights into the boundary structure of Wasserstein spaces over trees.

Abstract

We extend the geometric study of the Wasserstein space W(X) of a simply connected, negatively curved metric space X by investigating which pairs of boundary points can be linked by a geodesic, when X is a tree.