Fecha: 18 de Mayo del 2021
Expositor: Francisco Venegas

Título: Asymmetric free spaces

Resumen: Let (M, d) be a metric space. Consider a real-valued function f finitely supported on M with zero sum, that is \sum_{m\in M}f(m)=0.

This function can be regarded as a transportation problem, where each point m in M has either supply or demand of |f(m)|, depending on the sign of f(m). The vector space of transportation problems over M is endowed with a natural norm, which represents the optimal cost of transportation plans (representations of f) satisfying the transportation problem. These spaces are known by several names, including Transportaion Cost spaces, Wasserstein-1 spaces, Arens-Eells spaces and Lipschitz-free spaces, and have been studied by many authors using different approaches.

Many of the natural environments for transportation problems can be modeled using notions of distance which are not symmetric (and hence, not metrics), for instance, transportation problems where a vehicle needs to move through roads on a city, which often are unidirectional, or more generally, any transportation problem on a directed graph.

In this work we show that the notion of Transportation Cost spaces can be generalized to quasi-metric spaces, that is, sets endowed with distance functions which may not satisfy the symmetry assumption required to be a metric. The obtained Transportation Cost spaces, called Asymmetric free spaces enjoy the same fundamental properties of the classical Transportation Cost spaces, and can be used as a solid framework to study transportation problems in asymmetric spaces.

Link: https://uchile.zoom.us/j/82919875247?pwd=eWNhU0t2WFhrSnIyNmtrdWo3RUJxdz09
Clave: 206782