A1 Journal article (refereed)
Equivalent Definitions of Very Strict CD(K,N) -spaces (2023)

Schultz, T. (2023). Equivalent Definitions of Very Strict CD(K,N) -spaces. Journal of Geometric Analysis, 33(3), Article 108. https://doi.org/10.1007/s12220-022-01068-x

JYU authors or editors

Schultz, Timo

Publication details

All authors or editors: Schultz, Timo

Journal or series: Journal of Geometric Analysis

ISSN: 1050-6926

eISSN: 1559-002X

Publication year: 2023

Publication date: 30/01/2023

Volume: 33

Issue number: 3

Article number: 108

Publisher: Springer

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s12220-022-01068-x

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/85364

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1906.07693

Abstract

We show the equivalence of the definitions of very strict CD(K,N) -condition defined, on one hand, using (only) the entropy functionals, and on the other, the full displacement convexity class DCN. In particular, we show that assuming the convexity inequalities for the critical exponent implies it for all the greater exponents. We also establish the existence of optimal transport maps in very strict CD(K,N) -spaces with finite N.

Keywords: differential geometry

Free keywords: optimal transport; Ricci curvature; metric measure spaces

Fields of science: