eprintid: 10205629
rev_number: 7
eprint_status: archive
userid: 699
dir: disk0/10/20/56/29
datestamp: 2025-03-05 08:44:41
lastmod: 2025-03-05 08:44:41
status_changed: 2025-03-05 08:44:41
type: article
metadata_visibility: show
sword_depositor: 699
creators_name: Bellettini, Costante
creators_name: Marshall-Stevens, Kobe
title: On isolated singularities and generic regularity of min-max CMC hypersurfaces
ispublished: inpress
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
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 $\lambda$ 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.
date: 2025-07-01
date_type: published
publisher: Springer Verlag
full_text_type: other
language: eng
verified: verified_manual
elements_id: 2039865
lyricists_name: Bellettini, Costante
lyricists_id: CBELL94
actors_name: Bellettini, Costante
actors_id: CBELL94
actors_role: owner
funding_acknowledgements: EP/S005641/1 [Engineering and Physical Sciences Research Council]
full_text_status: restricted
publication: Journal of Geometric Analysis
issn: 1050-6926
citation:        Bellettini, Costante;    Marshall-Stevens, Kobe;      (2025)    On isolated singularities and generic regularity of min-max CMC hypersurfaces.                   Journal of Geometric Analysis           (In press).   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10205629/1/gen_reg_cmc_accepted.pdf