Related papers: Barycenters in Disintegrated optimal transport

Multimarginal optimal transport (MOT) has gained increasing attention in recent years, notably due to its relevance in machine learning and statistics, where one seeks to jointly compare and align multiple probability distributions. This…

Let (X,L) be a (semi-) polarized complex projective variety and T a real torus acting holomorphically on X with moment polytope P. Given a probability density g on P we introduce a new type of Monge-Ampere measure on X, defined for singular…

This paper consists of two results dealing with balanced metrics (in S. Donaldson terminology) on nonconpact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only…

By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry…

We show that there is generically non-uniqueness for the anisotropic Calder\'on problem at fixed frequency when the Dirichlet and Neumann data are measured on disjoint sets of the boundary of a given domain. More precisely, we first show…

We consider open discrete mappings of Riemannian manifolds that satisfy some modulus inequality. We investigate the possibility of a continuous extension of such mappings to an isolated point on the boundary. It is proved that, these…

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is…

This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumption is termed a variance inequality and…

We consider the multi-marginal optimal transport of aligning several compactly supported marginals on the Heisenberg group to minimize the total cost, which we take to be the sum of the squared Carnot-Carath\'eodory distances from the…

We study the geometry of the space of densities $\VolM$, which is the quotient space $\Diff(M)/\Diff_\mu(M)$ of the diffeomorphism group of a compact manifold $M$ by the subgroup of volume-preserving diffemorphisms, endowed with a…

First, we analyze the discrete Monge--Kantorovich problem, linking it with the minimization problem of linear functionals over adjoint orbits. Second, we consider its generalization to the setting of area preserving diffeomorphisms of the…

In this paper, we give a new characterization of the cut locus of a point on a compact Riemannian manifold as the zero set of the optimal transport density solution of the Monge-Kantorovich equations, a PDE formulation of the optimal…

The classical Kantorovich-Rubinstein duality theorem establishes a significant connection between Monge optimal transport and maximization of a linear form on the set of 1-Lipschitz functions. This result has been widely used in various…

We consider the Monge-Kantorovich problem between two random measuress. More precisely, given probability measures $\mathbb{P}_1,\mathbb{P}_2\in\mathcal{P}(\mathcal{P}(M))$ on the space $\mathcal{P}(M)$ of probability measures on a smooth…

Given a probability measure $\mu$ supported on a convex subset $\Omega$ of Euclidean space $(\mathbb{R}^d,g_0)$, we are interested in obtaining Poincar\'e and log-Sobolev type inequalities on $(\Omega,g_0,\mu)$. To this end, we change the…

We analyze statistical properties of plug-in estimators for unbalanced optimal transport quantities between finitely supported measures in different prototypical sampling models. Specifically, our main results provide non-asymptotic bounds…

Let $FM,\mathcal{M}_M$ be the bundles of linear frames and Riemannian metrics of a manifold $M$, respectively. The existence of a unique $\mathrm{Diff}M$-invariant connection form on $J^1\mathcal{M}_M\times_MFM\to J^1\mathcal{M}_M$, which…

We study cyclically monotone transport plans between measures in $\mathrm{M}_0(\mathbb{R}^d)$, the class of Borel measures on $\mathbb{R}^d \setminus \{0\}$ that are finite on sets bounded away from the origin but may have infinite total…

We give a concrete expression of a minimal singular metric of a big line bundle on a compact K\"ahler manifold which is the total space of a toric bundle over a complex torus. In this class of manifolds, Nakayama constructed examples which…

We study smooth bundles over surfaces with highly connected almost parallelizable fiber $M$ of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases,…