A Lipschitz map $f: \mathcal{C} \to H$ for the Hadamard space $H$. Sketch of the construction

Abstract

We introduce the sketch of construction of a Lipschitz function $f: \mathcal{C} \to H$, here the set $\mathcal{C}$ consists of all compact convex subsets of the Hadamard space $H$. Note that $f(\{x\})=\{x\}$ for any point $x \in H$.