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Existence of optimal transport maps in very strict \(CD(K,\infty )\) -spaces

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Abstract

We introduce a more restrictive version of the strict \(CD(K,\infty )\) -condition, the so-called very strict \(CD(K,\infty )\) -condition, and show the existence of optimal maps in very strict \(CD(K,\infty )\) -spaces despite the possible lack of uniqueness of optimal plans.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, 40014, University of Jvyäskylä, P.O. Box 35 (MaD), Jvyäskylä, Finland

    Timo Schultz

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  1. Timo Schultz
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Correspondence to Timo Schultz.

Additional information

Communicated by L. Ambrosio.

Author is partially supported by the Academy of Finland.

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Schultz, T. Existence of optimal transport maps in very strict \(CD(K,\infty )\) -spaces. Calc. Var. 57, 139 (2018). https://doi.org/10.1007/s00526-018-1414-y

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  • DOI: https://doi.org/10.1007/s00526-018-1414-y

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