Equivalent Definitions of Very Strict CD(K,N) -spaces
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.
Main Author
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202302061644Use this for linking
Review status
Peer reviewed
ISSN
1050-6926
DOI
https://doi.org/10.1007/s12220-022-01068-x
Language
English
Published in
Journal of Geometric Analysis
Citation
- 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
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Funder(s)
Research Council of Finland
Research Council of Finland
Funding program(s)
Research costs of Academy Research Fellow, AoF
Academy Project, AoF
Akatemiatutkijan tutkimuskulut, SA
Akatemiahanke, SA
Additional information about funding
The author also acknowledges the support by the Academy of Finland, projects #314789 and #312488. Funding Open Access funding provided by University of Jyväskylä (JYU).
Copyright© The Author(s) 2022