Spherical Localisation in Convex and Metric Geometry

TL;DR

This paper introduces spherical localisation, a geometric technique, and demonstrates its applications in convex and metric geometry, building on its historical development and relation to Euclidean localisation.

Contribution

It provides a concise introduction to spherical localisation and showcases its utility in solving problems within convex and metric geometry.

Findings

Spherical localisation is effective in convex geometry problems.

Applications demonstrate the technique's versatility.

The paper clarifies the relationship between spherical and Euclidean localisation.

Abstract

Spherical localisation is a technique whose history goes back to M.Gromov and V.Milman. It's counterpart, the Euclidean localisation is extensively studied and has been put to great use in various branches of mathematics. The purpose of this paper is to quickly introduce spherical localisation, as well as demonstrate some of its applications in convex and metric geometry.