2 papers
math.DG2025
The Riemannian geometry of the probability space of the unit circle
André Magalhães de Sá Gomes, Christian S. Rodrigues, Luiz A. B. San Martin
This paper explores the Riemannian geometry of the Wasserstein space of the circle, namely , the set of probability measures on the unit circle endowed with the 2-Wassers…
math.DG2025
On Differential and Riemannian Calculus on Wasserstein Spaces
André Magalhães de Sá Gomes, Christian S. Rodrigues, Luiz A. B. San Martin
In this paper we develop an intrinsic formalism to study the topology, smooth structure, and Riemannian geometry of the Wasserstein space of a closed Riemannian manifold. Our forma…