3 papers
math.OC2025
A synthetic approach to comparison principles for variational problems, with applications to optimal transport
Flavien Léger, Maxime Sylvestre
We develop a synthetic, variational framework for deriving comparison principles in infinite-dimensional Banach spaces. Unlike traditional approaches that rely on the regularity of…
math.MG2025
Nonnegative cross-curvature in infinite dimensions: synthetic definition and spaces of measures
Flavien Léger, Gabriele Todeschi, François-Xavier Vialard
Nonnegative cross-curvature (NNCC) is a geometric property of a cost function defined on a product space that originates in optimal transportation and the Ma-Trudinger-Wang theory.…
math.DG2024
A geometric approach to apriori estimates for optimal transport maps
Simon Brendle, Flavien Léger, Robert J. McCann +1
A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This tr…