Existence of Optimal Transport Maps with Applications in Metric Geometry
Julkaistu sarjassa
JYU dissertationsTekijät
Päivämäärä
2020Tekijänoikeudet
© The Author & University of Jyväskylä
Julkaisija
Jyväskylän yliopistoISBN
978-951-39-8183-9ISSN Hae Julkaisufoorumista
2489-9003Julkaisuun sisältyy osajulkaisuja
- Artikkeli I: Schultz, T. (2018). Existence of optimal transport maps in very strict CD(K,∞) -spaces. Calculus of Variations and Partial Differential Equations, 57 (5), 139. DOI: 10.1007/s00526-018-1414-y
- Artikkeli II: Rajala, T. and Schultz T.Optimal transport maps on Alexandrov spaces revisited. Preprint. arXiv:1803.10023
- Artikkeli III: Schultz, T. Equivalent definitions of very strict CD(K, N)-spaces. Preprint. arXiv:1906.07693
- Artikkeli IV: Schultz, T. On one-dimensionality of metric measure spaces. Proc. Amer. Math.Soc., to appear.
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- JYU Dissertations [748]
- Väitöskirjat [3426]
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Existence of optimal transport maps in very strict CD(K,∞) -spaces
Schultz, Timo (Springer Berlin Heidelberg, 2018)We introduce a more restrictive version of the strict CD(K,∞) -condition, the so-called very strict CD(K,∞) -condition, and show the existence of optimal maps in very strict CD(K,∞) -spaces despite the possible ... -
On one-dimensionality of metric measure spaces
Schultz, Timo (American Mathematical Society (AMS), 2021)In this paper, we prove that a metric measure space which has at least one open set isometric to an interval, and for which the (possibly non-unique) optimal transport map exists from any absolutely continuous measure to ... -
Infinitesimal Hilbertianity of Locally CAT(κ)-Spaces
Di Marino, Simone; Gigli, Nicola; Pasqualetto, Enrico; Soultanis, Elefterios (Springer, 2021)We show that, given a metric space (Y,d)(Y,d) of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure μμ on YY giving finite mass to bounded sets, the resulting metric measure space ... -
Quasispheres and metric doubling measures
Lohvansuu, Atte; Rajala, Kai; Rasimus, Martti (American Mathematical Society, 2018)Applying the Bonk-Kleiner characterization of Ahlfors 2-regular quasispheres, we show that a metric two-sphere X is a quasisphere if and only if X is linearly locally connected and carries a weak metric doubling measure, ... -
Quasiconformal Jordan Domains
Ikonen, Toni (Walter de Gruyter GmbH, 2021)We extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y,dY). We say that a metric space (Y,dY) is a quasiconformal Jordan domain if the completion Y of (Y,dY) has finite Hausdor 2-measure, ...
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