A survey of mass partitions

TL;DR

This survey reviews recent advances in mass partition problems, exploring their connections to topology, discrete geometry, and computer science, and highlighting key developments in the field.

Contribution

It provides a comprehensive overview of recent progress and interdisciplinary links in the study of mass partition problems.

Findings

Recent progress in mass partition problem solutions

Connections between mass partitions and topology established

Applications in computer science and discrete geometry identified

Abstract

Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this survey we describe recent progress in the area in addition to its connections to topology, discrete geometry, and computer science.