Some results about the Tight Span of spheres

TL;DR

This paper investigates the properties of the tight span of n-spheres under different metrics, contributing to the understanding of hyperconvex spaces in metric geometry and data analysis.

Contribution

It provides new insights into the structure of tight spans specifically for n-spheres with geodesic and l-infinity metrics.

Findings

Characterization of tight spans of n-spheres

Comparison between geodesic and l-infinity metrics

Implications for metric geometry and data analysis

Abstract

The smallest hyperconvex metric space containing a given metric space X is called the tight span of X. It is known that tight spans have many nice geometric and topological properties, and they are gradually becoming a target of research of both the metric geometry community and the topological/geometric data analysis community. In this paper, we study the tight span of n-spheres (with either geodesic metric or l infinity-metric).