Proves that if the forward Lax-Oleinik evolution Tu is locally semiconcave near a point with future-directed timelike superdifferentials, then a further evolution yields a locally C^{1,1} function, applied to optimal transport duality.
On the locus of multiple maximizing geodesics on a globally hyperbolic spacetime.arXiv preprint arXiv:2507.22737, 2025
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A Lorentzian Lasry-Lions regularization theorem
Proves that if the forward Lax-Oleinik evolution Tu is locally semiconcave near a point with future-directed timelike superdifferentials, then a further evolution yields a locally C^{1,1} function, applied to optimal transport duality.