English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This note exposes the differential topology and geometry underlying some ofthe basic phenomena of optimal transportation. It surveys basic questionsconcerning Monge maps and Kantorovich measures: existence and regularity of theformer, uniqueness of the latter, and estimates for the dimension of itssupport, as well as the associated linear programming duality. It shows theanswers to these questions concern the differential geometry and topology ofthe chosen transportation cost. It also establishes new connections --- someheuristic and others rigorous --- based on the properties of thecross-difference of this cost, and its Taylor expansion at the diagonal.

A glimpse into the differential topology and geometry of optimal transport