@article{discovery10205629,
           month = {July},
           title = {On isolated singularities and generic regularity of min-max CMC hypersurfaces},
            note = {This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.},
         journal = {Journal of Geometric Analysis},
            year = {2025},
       publisher = {Springer Verlag},
          author = {Bellettini, Costante and Marshall-Stevens, Kobe},
             url = {https://discovery.ucl.ac.uk/id/eprint/10205629/},
            issn = {1050-6926},
        abstract = {In compact Riemannian manifolds of dimension 3 or higher with positive Ricci
curvature, we prove that every constant mean curvature hypersurface produced by
the Allen-Cahn min-max procedure of Bellettini-Wickramasekera (with constant
prescribing function) is a local minimiser of the natural area-type functional
around each isolated singularity. In particular, every tangent cone at each
isolated singularity of the resulting hypersurface is area-minimising. As a
consequence, for any real \${$\backslash$}lambda\$ we show, through a surgery procedure, that
for a generic 8-dimensional compact Riemannian manifold with positive Ricci
curvature there exists a closed embedded smooth hypersurface of constant mean
curvature \${$\backslash$}lambda\$; the minimal case (\${$\backslash$}lambda\$ = 0) of this result was
obtained in work by Chodosh-Liokumovich-Spolaor.}
}