The n-point Condition and Rough CAT(0)

TL;DR

This paper establishes an equivalence between the rough n-point condition for length spaces and the rough CAT(0) property, providing a new characterization for these geometric conditions.

Contribution

It proves that for n > 4, a length space satisfies the rough n-point condition if and only if it is rough CAT(0), linking two important geometric concepts.

Findings

Equivalence between rough n-point condition and rough CAT(0) for n > 4

Provides a new characterization of rough CAT(0) spaces

Advances understanding of metric space curvature conditions

Abstract

We show that for n > 4 a length space (X,d) satisfies a rough n-point condition if and only it it is rough CAT(0).