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math.AP2026
Caffarelli Estimates under Lipschitz Perturbations
Maja Gwóźdź
We study dimension-free differential estimates for Brenier maps under first-order perturbations of the two marginals. Caffarelli's contraction theorem yields such estimates when th…
math.AP2026
Dimension-Free Lipschitz Bounds for Brenier Maps to Compactly Supported Log-Concave Targets
Maja Gwozdz
We fix an integer and a symmetric positive-definite matrix . Let be finite, set \[ Z_μ:=\int_{\mathbb{R}^d}e^{-V(x…
math.AP2026
Sharp Continuity Moduli for Dirichlet Heat Flow in Boundary-Reservoir Transport Metrics
Maja Gwozdz
Let be a bounded open set and let be the killed Dirichlet heat semigroup. We prove the sharp fixed-time power-scale modulus of for the Figal…
math.AP2026
Instability of the ray-monotone selector for -optimal transport
Maja Gwozdz
For the distance cost , the set of -optimal plans is generally not a singleton. Under the classical absolute-continuity hypotheses in the Euclidean case…