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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We introduce the setting of extended metric-topological measure spaces as ageneral "Wiener-like" framework for optimal transport problems and nonsmoothmetric analysis in infinite dimension.  After a brief review of optimal transport tools for general Radon measures,we discuss the notions of the Cheeger energy, of the Radon measuresconcentrated on absolutely continuous curves, and of the induced "dynamictransport distances." We study their main properties and their links with thetheory of Dirichlet forms and the Bakry-\'Emery curvature condition, inparticular concerning the contractivity properties and the EVI formulation ofthe induced Heat semigroup.

Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces