Roundness properties of ultrametric spaces

TL;DR

This paper explores new characterizations of ultrametric spaces using roundness and related properties, providing insights into their isometric embedding into Euclidean spaces and examining non-ultrametric additive metric spaces.

Contribution

It introduces novel characterizations of ultrametric spaces through roundness and generalized properties, enhancing understanding of their geometric embeddings.

Findings

New characterizations of ultrametric spaces in terms of roundness and p-negative type

Insights into isometric embedding of ultrametric spaces into Euclidean spaces

Analysis of roundness properties in additive metric spaces that are not ultrametric

Abstract

We obtain several new characterizations of ultrametric spaces in terms of roundness, generalized roundness, strict p-negative type, and p-polygonal equalities (p > 0). This allows new insight into the isometric embedding of ultrametric spaces into Euclidean spaces. We also consider roundness properties additive metric spaces which are not ultrametric.