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Ball Intersection Properties in Metric Spaces
Benjamin Miesch, Maël Pavón
We show that in complete metric spaces, -hyperconvexity is equivalent to finite hyperconvexity. Moreover, every complete, almost -hyperconvex metric space is -hyperconvex.…
Injective Subsets of
Dominic Descombes, Maël Pavón
We give an explicit characterization of all injective subsets of the model space for a general set , in terms of inequalities involving -Lipschitz functions.…
Weakly Externally Hyperconvex Subsets and Hyperconvex Gluings
Benjamin Miesch, Maël Pavón
We give a necessary and sufficient condition for gluings of hyperconvex metric spaces along weakly externally hyperconvex subsets in order that the resulting space be hyperconvex.…
Injective Hulls of Infinite Totally Split-Decomposable Metric Spaces
Maël Pavón
We consider the class of (possibly) infinite metric spaces with integer-valued totally split-decomposable metric and possessing an injective hull which has the structure of a polyh…
Injective Convex Polyhedra
Maël Pavón
It was shown by Nachbin in 1950 that an -dimensional normed space is injective or equivalently is an absolute 1-Lipschitz retract if and only if is linearly isometric to…
Metric stability of trees and tight spans
Urs Lang, Maël Pavón, Roger Züst
In this note, we prove optimal extension results for roughly isometric relations between metric (R-)trees and injective metric spaces. This yields sharp stability estimates, in ter…