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 $x\in H$.

Brief note