Lipschitz L² stability estimates for OT maps in terms of 2-MK distance (and C^{1,α} under Hölder) plus explicit second variation of quadratic MK distance via Monge-Ampère linearization.
arXiv preprint arXiv:2507.05395 , year=
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Constructs solutions to Monge-Ampère equations with singular measure components on low-codimension sets, studies their regularity, and motivates the work with optimal transport examples.
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Stability of optimal transport maps and second variation of the 2-Monge-Kantorovich distance
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