Preprint

Inserted: 18 jul 2025
Last Updated: 18 jul 2025

Year: 2025

Abstract:

We construct partitions of $\mathbb{R}^n$ into three sets $\{\mathcal{X}(1),\mathcal{X}(2),\mathcal{X}(3)\}$ that locally minimize interfacial area among compactly supported volume preserving variations and that blow down at infinity to singular area-minimizing cones. As a consequence, we prove the non-uniqueness of the standard lens cluster in a large number of dimensions starting from $8$.

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• main.pdf
• supplementarycode.cpp
• supplementarytable.txt