Preprint
Inserted: 5 jul 2026
Last Updated: 5 jul 2026
Year: 2026
Abstract:
We prove a quantitative stability of Kantorovich potentials on non-smooth metric measure spaces with synthetic lower Ricci curvature bound, thereby confirming a recent conjecture of Kitagawa, Letrouit and M\'erigot. Our proof, which employs the heat kernel-regularized $c$-transform, does not rely on linear structure or sectional curvature bounds, is new even in the smooth setting. As a corollary, we get a quantitative stability of optimal transport maps on Alexandrov spaces with lower curvature bound.
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