Global Lipschitz extension preserving the slope

Jacopo Somaglia (Politecnico di Milano)

Abstract: We show that every real-valued Lipschitz function on a subset of a metric space can be extended to the whole space while preserving the slope and, up to a small error, the global Lipschitz constant. This answers a question posed by Di Marino, Gigli, and Pratelli, who established the analogous property for the asymptotic Lipschitz constant. This is a joint work with Nicolò De Ponti.