We study the Daugavet property in the space of Lipschitz functions Lip 0 (M) on a complete
metric space M. Namely we show that Lip 0 (M) has the Daugavet property if and only if M is …

We study the set SNA (M, Y) of those Lipschitz maps from a (complete pointed) metric space
M to a Banach space Y which (strongly) attain their Lipschitz norm (ie the supremum …

We show that the class of Lipschitz-free spaces over closed subsets of any complete metric
space M is closed under arbitrary intersections, improving upon the previously known finite …

We analyse the relationship between different extremal notions in Lipschitz free spaces
(strongly exposed, exposed, preserved extreme and extreme points). We prove in particular …

For a complete metric space M, we prove that the finitely supported extreme points of the unit
ball of the Lipschitz-free space F (M) are precisely the elementary molecules (δ (p)− δ (q))/d …

We study Daugavet points and $\Delta $-points in Lipschitz-free Banach spaces. We prove
that, if $ M $ is a compact metric space, then $\mu\in S_ {\mathcal F (M)} $ is a Daugavet …

Abstract A norm $1 $ element $ x $ of a Banach space is a Daugavet point (respectively, a
$\Delta $-point) if every slice of the unit ball (respectively, every slice of the unit ball …

A metric space M is length when every two points have an approximate midpoint, while M
has property (Z) when for every x, y∈ M there exists z such that d (x, z)+ d (z, y)− d (x, y) is …

We study the density of the set SNA (M, Y) of those Lipschitz maps from a (complete pointed)
metric space M to a Banach space Y which strongly attain their norm (ie, the supremum …

We survey recent progress on three relevant instances of free objects related to Banach
spaces: Lipschitz free spaces generated by metric spaces, holomorphic free spaces …