Abstract
AbstractWe propose a generalized curvature that is motivated by the optimal transport problem on $${\mathbb {R}}^d$$
R
d
with cost induced by a Tonelli Lagrangian L. We show that non-negativity of the generalized curvature implies displacement convexity of the generalized entropy functional on the L-Wasserstein space along $$C^2$$
C
2
displacement interpolants.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference21 articles.
1. Agueh, M.: Sharp Gagliardo–Nirenberg inequalities and mass transport theory. J. Dyn. Differ. Equ. 18, 1069–1093 (2006)
2. Ambrosio, L., Gigli, N., Savaré, G.: Gradient Flows in Metric Spaces and in the Space of Probability Measures. Birkhäuser, New York (2005)
3. Bauer, M., Modin, K.: Semi-invariant Riemannian metrics in hydrodynamics. Calc. Var. Partial. Differ. Equ. 59(2), Paper No. 65, 25 pp. (2020)
4. Benamou, J.-D., Brenier, Y.: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84, 375–393 (2000)
5. Bernard, P., Buffoni, B.: Optimal mass transportation and Mather theory. J. Eur. Math. Soc. 9, 85–121 (2007)