Diameter bounded equal measure partitions of Ahlfors regular metric measure spaces

TL;DR

This paper presents a new partition algorithm for connected Ahlfors regular metric measure spaces that combines existing methods to produce equal measure partitions with bounded diameter.

Contribution

It introduces a novel partitioning algorithm applicable to any connected Ahlfors regular metric measure space of finite measure, extending prior sphere-specific methods.

Findings

Algorithm successfully partitions spaces into equal measure regions with bounded diameter

Applicable to a wide class of Ahlfors regular metric measure spaces

Extends sphere partitioning techniques to more general spaces

Abstract

The algorithm devised by Feige and Schechtman for partitioning higher dimensional spheres into regions of equal measure and small diameter is combined with David and Christ's construction of dyadic cubes to yield a partition algorithm suitable to any connected Ahlfors regular metric measure space of finite measure.