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arXiv · 2507.13995

On the non-uniqueness of locally minimizing clusters via singular cones

Lia Bronsard·Robin Neumayer·Michael Novack·Anna Skorobogatova
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Abstract

We construct partitions of $\mathbb{R}^n$ into three sets $\{\mathscr{X}(1),\mathscr{X}(2),\mathscr{X}(3)\}$ 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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Lia Bronsard, Robin Neumayer, Michael Novack, Anna Skorobogatova. 2025-07-18. On the non-uniqueness of locally minimizing clusters via singular cones. https://arxiv.org/abs/2507.13995

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