caa a22 4500 445843675 CHVBK 20180317145352.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00526-011-0395-x doi (NATIONALLICENCE)springer-10.1007/s00526-011-0395-x Wolansky G. Department of Mathematics, Technion, 32000, Haifa, Israel aut Limit theorems for optimal mass transportation [Elektronische Daten] [G. Wolansky] The optimal mass transportation was introduced by Monge some 200years ago and is, today, the source of large number of results in analysis, geometry and convexity. Here I investigate a new, surprising link between optimal transformations obtained by different Lagrangian actions on Riemannian manifolds. As a special case, for any pair of non-negative measures λ+, λ− of equal mass $$W_1(\lambda^-, \lambda^+)= \lim_{\varepsilon\rightarrow 0} \varepsilon^{-1} \inf_{\mu} W_p(\mu+\varepsilon\lambda^-, \mu+\varepsilon\lambda^+) $$where W p, p≥ 1 is the Wasserstein distance and the infimum is over the set of probability measures in the ambient space. Springer-Verlag, 2011 Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 487-516 0944-2669 42:3-4<487 2011 42 526 https://doi.org/10.1007/s00526-011-0395-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-011-0395-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wolansky G. Department of Mathematics, Technion, 32000, Haifa, Israel aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 42/3-4(2011-11-01), 487-516 0944-2669 42:3-4<487 2011 42 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer