Absolute Lipschitz extendability and linear projection constants

Abstract

We prove that the absolute extendability constant of a finite metric space may be determined by computing relative projection constants of certain Lipschitz-free spaces. As an application, we show that ae(3) = 4/3 and ae(4) ≥ (5 + 4 √2)/7. Moreover, we discuss how to compute relative projection constants by solving linear programming problems.