Optimal-diameter partitions into regions of the prescribed measure

Grigory Voinov

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arXiv · 2609.23867

Optimal-diameter partitions into regions of the prescribed measure

Grigory Voinov

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Abstract

In this paper we find a sufficient condition on an Ahlfors--David regular metric measure space under which it admits a partition into parts of prescribed measures and optimal (up to a constant) diameters. The proof uses the construction of dyadic cubes. The process is algorithmic: the pieces are cut out one by one via a filling procedure on the tree of dyadic cubes. We introduce the notion of spaces which admit a connected dyadic cube decomposition and prove that they admit a partition of the kind described above. We then develop several techniques to obtain such spaces and show some natural examples of this type.

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BibTeX RIS

Grigory Voinov. 2026-09-20. Optimal-diameter partitions into regions of the prescribed measure. https://arxiv.org/abs/2609.23867

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