Equivalent Definitions of Very Strict CD(K,N) -spaces
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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Journal of Geometric AnalysisDate
2023Copyright
© The Author(s) 2022
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.
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https://converis.jyu.fi/converis/portal/detail/Publication/176708933
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Research Council of FinlandFunding program(s)
Research costs of Academy Research Fellow, AoF; Academy Project, AoFAdditional 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).License
Except where otherwise noted, this item's license is described as CC BY 4.0