Energy Bounds for Kantorovich Transport Distances with Convex Cost Functions
Sergey Bobkov, Friedrich G\"otze
TL;DR
This paper develops energy bounds for Kantorovich transport distances with convex costs, extending previous estimates for $W_p$ distances, thereby providing new theoretical insights into optimal transport metrics.
Contribution
It introduces generalized energy bounds for Kantorovich distances with convex cost functions, expanding upon Ledoux's estimates for $W_p$ distances.
Findings
Extended energy bounds for Kantorovich transport distances.
Generalized estimates for convex cost functions.
Enhanced theoretical understanding of optimal transport metrics.
Abstract
Energy bounds for Kantorovich transport distances are developed for convex cost functions. The main results extend estimates due to M. Ledoux for the Kantorovich distances .
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Taxonomy
TopicsOptimization and Variational Analysis · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations