相关论文: Kantorovich Duality and Optimal Transport Problems…

This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…

The graph layouts used for complex network studies have been mainly been developed to improve visualization. If we interpret the layouts in metric spaces such as Euclidean ones, however, the embedded spatial information can be a valuable…

Given $\phi$ a pseudo-Anosov map, let $\ell_\mathcal{T}(\phi)$ denote the translation length of $\phi$ in the Teichm\"uller space, and let $\ell_\mathcal{C}(\phi)$ denote the stable translation length of $\phi$ in the curve graph.…

A central role in topological dimension theory is played by Lipscomb's space $J_{A}$ since it is a universal space for metric spaces of weight $|A|\geq \aleph _{0}$. On the one hand, Lipscomb's space is the attractor of a possibly infinite…

In finite graphs, finite-order tangles offer an abstract description of highly connected substructures. In infinite graphs, infinite-order tangles compactify the graphs in the same way the ends compactify connected locally finite graphs.…

We resolve the existence of mixed 't Hooft anomalies between the electric and magnetic (solitonic) symmetries in $\sigma$-models and gauge theories. We identify the anomaly as naturally originating from a higher group in the Whitehead tower…

Spacetimes obtained by dimensional reduction along lattices containing a lightlike direction can admit semigroup extensions of their isometry groups. We show by concrete examples that such a semigroup can exhibit a natural order, which in…

We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…

We present a contravariant reflection of the compact $T_1$-spaces with arrows given by closed continuous functions into the category of bounded distributive lattices with arrows given by closed subfit morphisms. This reflection extends both…

A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for \textsc{Maximum Clique} on unit disk graphs [Clark, Colbourn, Johnson; Discrete…

We show that, on a $2$-dimensional compact manifold, the optimal transport map in the semi-discrete random matching problem is well-approximated in the $L^2$-norm by identity plus the gradient of the solution to the Poisson problem $-\Delta…

In this work we provide a characterization of distinct type of (linear and non-linear) maps between Banach spaces in terms of the differentiability of certain class of Lipschitz functions. Our results are stated in an abstract bornological…

We study three approaches to electric-magnetic duality in the 4-dimensional Maxwell theory coupled to a dyonic point charge and in the 5-dimensional Maxwell-Chern-Simons (MCS) theory coupled to an electric point charge and a magnetic string…

The cut pseudo-metric on the space of graph limits induces an equivalence relation. The quotient space obtained by collapsing each equivalence class to a point is a metric space with appealing analytic properties. We show that the…

Using optimal transport we study some dynamical properties of expanding circle maps acting on measures by push-forward. Using the definition of the tangent space to the space of measures introduced by Gigli, their derivative at the unique…

A semiclassical theory based on the Boltzmann transport equation for a two-dimensional electron gas modulated along one direction with weak electrostatic or magnetic modulations is proposed. It is shown that oscillations of the…

We study optimal transportation of measures on compact manifolds for costs defined from convex Lagrangians. We prove that optimal transportation can be interpolated by measured Lipschitz laminations, or geometric currents. The methods are…

We formulate and study an optimal transportation problem with infinitely many marginals; this is a natural extension of the multi-marginal problem studied by Gangbo and Swiech (1998). We prove results on the existence, uniqueness and…

We introduce and study the class of linear transfers between probability distributions and the dual class of Kantorovich operators between function spaces. Linear transfers can be seen as an extension of convex lower semi-continuous…

We prove that the outer $L^p_\mu(\ell^r)$ spaces, introduced by Do and Thiele, are isomorphic to Banach spaces, and we show the expected duality properties between them for $1 < p \leq \infty, 1 \leq r < \infty$ or $p=r \in \{ 1, \infty \}$…