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<https://discovery.ucl.ac.uk/id/eprint/10205629> <http://purl.org/dc/terms/title> "On isolated singularities and generic regularity of min-max CMC hypersurfaces"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10205629> <http://purl.org/ontology/bibo/abstract> "In compact Riemannian manifolds of dimension 3 or higher with positive Ricci\r\ncurvature, we prove that every constant mean curvature hypersurface produced by\r\nthe Allen-Cahn min-max procedure of Bellettini-Wickramasekera (with constant\r\nprescribing function) is a local minimiser of the natural area-type functional\r\naround each isolated singularity. In particular, every tangent cone at each\r\nisolated singularity of the resulting hypersurface is area-minimising. As a\r\nconsequence, for any real $\\lambda$ we show, through a surgery procedure, that\r\nfor a generic 8-dimensional compact Riemannian manifold with positive Ricci\r\ncurvature there exists a closed embedded smooth hypersurface of constant mean\r\ncurvature $\\lambda$; the minimal case ($\\lambda$ = 0) of this result was\r\nobtained in work by Chodosh-Liokumovich-Spolaor."^^<http://www.w3.org/2001/XMLSchema#string> .
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