caa a22 4500 445843314 CHVBK 20180317145351.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s00526-010-0362-y doi (NATIONALLICENCE)springer-10.1007/s00526-010-0362-y The Ma-Trudinger-Wang curvature for natural mechanical actions [Elektronische Daten] [Paul Lee, Robert McCann] The Ma-Trudinger-Wang curvature—or cross-curvature—is an object arising in the regularity theory of optimal transportation. If the transportation cost is derived from a Hamiltonian action, we show its cross-curvature can be expressed in terms of the associated Jacobi fields. Using this expression, we show the least action corresponding to a harmonic oscillator has zero cross-curvature, and in particular satisfies the necessary and sufficient condition (A3w) for the continuity of optimal maps. We go on to study gentle perturbations of the free action by a potential, and deduce conditions on the potential which guarantee either that the corresponding cost satisfies the more restrictive condition (A3s) of Ma, Trudinger and Wang, or in some cases has positive cross-curvature. In particular, the quartic potential of the anharmonic oscillator satisfies (A3s) in the perturbative regime. Springer-Verlag, 2010 Lee Paul Department of Mathematics, University of California at Berkeley, 970 Evans Hall #3840, 94720-3840, Berkeley, CA, USA aut McCann Robert Department of Mathematics, University of Toronto, M5S 2E4, Toronto, ON, Canada aut Calculus of Variations and Partial Differential Equations Springer-Verlag 41/1-2(2011-05-01), 285-299 0944-2669 41:1-2<285 2011 41 526 https://doi.org/10.1007/s00526-010-0362-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0362-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lee Paul Department of Mathematics, University of California at Berkeley, 970 Evans Hall #3840, 94720-3840, Berkeley, CA, USA aut NATIONALLICENCE 700 1- McCann Robert Department of Mathematics, University of Toronto, M5S 2E4, Toronto, ON, Canada aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 41/1-2(2011-05-01), 285-299 0944-2669 41:1-2<285 2011 41 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer