Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Marshall-Stevens, Kobe, Niu, Gongping
Institutions: Johns Hopkins University, University of Rochester
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221539854