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arXiv · 2308.04999

Generalized curvature for the optimal transport problem induced by a Tonelli Lagrangian

Yuchuan Yang
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Abstract

We propose a generalized curvature that is motivated by the optimal transport problem on $\mathbb{R}^d$ 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 $C^2$ displacement interpolants.

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Yuchuan Yang. 2023-08-09. Generalized curvature for the optimal transport problem induced by a Tonelli Lagrangian. https://doi.org/10.1007/s00526-023-02550-2

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