Morse subsets of CAT(0) spaces are strongly contracting

TL;DR

This paper proves that Morse subsets in CAT(0) spaces are strongly contracting, generalizing previous results for Morse quasi-geodesics and simplifying the proof using recurrence characterization.

Contribution

It extends the understanding of Morse subsets in CAT(0) spaces by establishing their strong contraction property with a simplified proof.

Findings

Morse subsets in CAT(0) spaces are strongly contracting

The proof uses recurrence characterization of Morse subsets

Generalizes previous results for Morse quasi-geodesics

Abstract

We prove that Morse subsets of CAT(0) spaces are strongly contracting. This generalizes and simplifies a result of Sultan, who proved it for Morse quasi-geodesics. Our proof goes through the recurrence characterization of Morse subsets.