Majorization in spaces with a curved geometry

TL;DR

This paper extends the Hardy-Littlewood-P?olya majorization theorem to curved geometric spaces like NPC and Wasserstein spaces, exploring its relation to Schur convexity.

Contribution

It introduces a new form of majorization applicable to curved spaces and links it to Schur convexity, broadening the theorem's scope.

Findings

Majorization concept adapted to NPC and Wasserstein spaces

Established connection between majorization and Schur convexity in curved spaces

Extended classical inequalities to non-Euclidean geometries

Abstract

The Hardy-Littlewood-P?olya majorization theorem is extended to the framework of some spaces with a curved geometry (such as the global NPC spaces and the Wasserstein spaces). We also discuss the connection between our concept of majorization and the subject of Schur convexity.