Closed mean curvature flows with asymptotically conical singularities
Abstract
In this paper, we prove that for any asymptotically conical selfshrinker, there exists an embedded closed hypersurface such that the mean curvature flow starting from it develops a singularity modeled on the given shrinker. The main technique is the Ważewski box argument, used by Stolarski in the proof of the corresponding theorem in the Ricci flow case. As a corollary, our construction, combined with the works of AngenentIlmanenVelázquez and ChodoshDanielsHolgateSchulze, implies the existence of fattening level set flows starting from smooth embedded closed hypersurfaces. This addresses a question posed by EvansSpruck and De Giorgi.
 Publication:

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.15577
 arXiv:
 arXiv:2405.15577
 Bibcode:
 2024arXiv240515577L
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs
 EPrint:
 21 pages