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arXiv · 2610.13423

Isoperimetry of singular CMC hypersurfaces

Kobe Marshall-Stevens·Gongping Niu
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Abstract

We produce the first examples of singular isoperimetric boundaries with non-zero constant mean curvature in Riemannian manifolds. The main technical ingredient is establishing that, for constant mean curvature hypersurfaces containing isolated singularities modelled on strictly stable, strictly minimising regular tangent cones, weak strict stability implies local unique volume-constrained minimisation.

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Kobe Marshall-Stevens, Gongping Niu. 2026-10-09. Isoperimetry of singular CMC hypersurfaces. https://arxiv.org/abs/2610.13423

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