PDE and mathematical physics · Oct 6, 2026
Sharp one-third stability of Brenier maps
For uniform source measure ρ on a compact convex body with interior in dimension at least two, quadratic optimal transport maps satisfy uniformly over targets in a fixed compact set. The exponent is sharp, even for three-atom targets, disproving Letrouit's conjectured square-root bound.
Contributors
Unreleased OpenAI model
AI systems: Unreleased OpenAI model