相关论文: Kantorovich Duality and Optimal Transport Problems…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
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…
Given a Banach lattice $L,$ the space of lattice Lipschitz operators on $L$ has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is…
Masur and Minsky showed that the curve graph is quasi-isometric to the Teichm\"uller space electrified along its thin part, and hence the Teichm\"uller space is weakly relatively hyperbolic with respect to the thin part. In this paper, we…
Let $\Gamma$ be a graph. Under suitable geometric assumptions on $\Gamma$, we give several equivalent characterizations of Sobolev and Hardy-Sobolev spaces on $\Gamma$, in terms of maximal functionals, Haj{\l} asz type functionals or atomic…
Since the seminal work of Schoen-Uhlenbeck, many authors have studied properties of harmonic maps satisfying Dirichlet boundary conditions. In this article, we instead investigate regularity and symmetry of $\mathbb{S}^2-$valued minimizing…
In the Engel group with its Carnot group structure we study subsets of locally finite subRiemannian perimeter and possessing constant subRiemannian normal. We prove the rectifiability of such sets: more precisely we show that, in some…
We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the…
We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a…
We show that both separable preduals of $L_{1}$ and non-type I $C^*$-algebras are strictly extremal with respect to the minimal displacement of $k$-Lipschitz mappings acting on the unit ball of a Banach space. In particular, every separable…
The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various…
A single-parameter family of lattice-fermion model is constructed. It is a deformation of the Azbel-Hofstadter problem by a parameter $h={$B%((BDelta}/t$ (quantum parameter). A topological number is attached to each energy band. A duality…
We study the optimal transport problem on globally hyperbolic spacetimes associated with Orlicz-type Lorentzian cost functions of the form $u \circ \ell$, where $u$ is a suitable monotonically increasing and concave function, and $\ell$ is…
In this paper, we study geometric properties of $\ell^{p}$-spaces associated with the unitary dual of a compact group. More precisely, we prove uniform smoothness, uniform convexity, Clarkson type inequalities, Kadec-Klee property, as well…
We investigate the duality structure of quantum lattice systems with topological order, a collective order also appearing in fractional quantum Hall systems. We define electromagnetic (EM) duality for all of Kitaev's quantum double models…
An $\ell$-lift of a graph $G$ is any graph obtained by replacing every vertex of $G$ with an independent set of size $\ell$, and connecting every pair of two such independent sets that correspond to an edge in $G$ by a matching of size…
We use localization to compute the partition function of a four dimensional, supersymmetric, abelian gauge theory on a hemisphere coupled to charged matter on the boundary. Our theory has eight real supercharges in the bulk of which four…
This paper deals with the large-scale behaviour of dynamical optimal transport on $\mathbb{Z}^d$-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes…
Two field 2-forms on the space-time manifold, in a relationship of duality, are presented and included in the extended phase-space structure used to describe relativistic particles having both electric and magnetic charges. By exterior…
We construct a compact minitwistor space from a hyperelliptic curve with real structure and show that it yields a lot of new Lorentzian Einstein-Weyl spaces all of which are diffeomorphic to the 3-dimensional deSitter space. These…