This is an announcement for the paper “On exposed points of Lipschitz free spaces” by Colin Petitjeanhttps://arxiv.org/search/math?searchtype=author&query=Petitjean%2C+C, Antonín Procházkahttps://arxiv.org/search/math?searchtype=author&query=Proch%C3%A1zka%2C+A.
Abstract: In this note we prove that a molecule $d(x,y)^{-1}(δ(x)-δ(y))$ is an exposed point of the unit ball of a Lispchitz free space $\mathcal F(M)$ if and only if the metric segment $[x,y]={z \in M ; : ; d(x,y)=d(z,x)+d(z,y) }$ is reduced to ${x,y}$. This is based on a recent result due to Aliaga and Pernecká which states that the class of Lipschitz free spaces over closed subsets of M is closed under arbitrary intersections when M has finite diameter.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1810.12031