Five lectures on optimal transportation: Geometry, regularity and applications
Analysis of PDEs
2010-11-15 v1 Differential Geometry
Abstract
In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y). Connections to geometry, inequalities, and partial differential equations will be discussed, focusing in particular on recent developments in the regularity theory for Monge-Ampere type equations. An application to microeconomics will also be described, which amounts to finding the equilibrium price distribution for a monopolist marketing a multidimensional line of products to a population of anonymous agents whose preferences are known only statistically.
Cite
@article{arxiv.1011.2911,
title = {Five lectures on optimal transportation: Geometry, regularity and applications},
author = {Nestor Guillen and Robert McCann},
journal= {arXiv preprint arXiv:1011.2911},
year = {2010}
}