Existence of Optimal Transport Maps with Applications in Metric Geometry
- 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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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 ...
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 ...
Bonicatto, Paolo; Pasqualetto, Enrico; Rajala, Tapio (Springer, 2020)We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak (1,1)-Poincaré inequality. The two main results we obtain are a decomposition ...
Arroyo, Ángel; Llorente, José G. (American Mathematical Society, 2019)A metric measure space (X, d, t) is said to satisfy the strong annular decay condition if there is a constant C > 0 such that for each x E X and all 0 < r < R. If do., is the distance induced by the co -norm in RN, we ...
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, ...