7 papers
On Foliated Optimal Transport
Diego S. Ledesma, Renata Possobon, Christian S. Rodrigues
In this paper we introduce a geometrically constrained optimal transport problem on Riemannian manifolds endowed with a Borel foliation, in which mass is transported only within in…
The Wasserstein space of the circle is not flat
André Magalhães de Sá Gomes, Christian S. Rodrigues, Luiz A. B. San Martin
We show that the Wasserstein space of the circle is not flat, in contrast with the flatness of the Wasserstein spaces of the real line and of an interval. Its sectional curvature i…
Pushforward dynamics on Wasserstein spaces and measure rigidity
Douglas Finamore, André Magalhães de Sá Gomes, Christian S. Rodrigues
For an endomorphism of a closed Riemannian manifold , we study the pushforward action on the Wasserstein space at a measure preserved by .…
Characterization of foliations via disintegration maps
Florentin Münch, Renata Possobon, Christian S. Rodrigues
In this paper, we present a novel approach for analyzing the relationship between the supports of conditional measures and their geometric arrangement in Wasserstein space via the…
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…
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…
Displacement convexity of Invariant Measures and curvature bounds of isometric actions
André Magalhães de Sá Gomes, Christian S. Rodrigues
Let be a proper isometric action of a compact Lie group on a complete, connected and orientable Riemannian manifold of dimension . We characterize the loca…