TY  - INPR
Y1  - 2025/07/01/
AV  - restricted
TI  - On isolated singularities and generic regularity of min-max CMC hypersurfaces
N1  - This version is the author accepted manuscript. For information on re-use, please refer to the publisher?s terms and conditions.
UR  - https://discovery.ucl.ac.uk/id/eprint/10205629/
PB  - Springer Verlag
SN  - 1050-6926
N2  - 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 $\lambda$ 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 $\lambda$; the minimal case ($\lambda$ = 0) of this result was
obtained in work by Chodosh-Liokumovich-Spolaor.
ID  - discovery10205629
A1  - Bellettini, Costante
A1  - Marshall-Stevens, Kobe
JF  - Journal of Geometric Analysis
ER  -