Closed mean curvature flows with asymptotically conical singularities

Autor:	Lee, Tang-Kai, Zhao, Xinrui
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	In this paper, we prove that for any asymptotically conical self-shrinker, 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 Wa\.zewski 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 Angenent--Ilmanen--Vel\'azquez and Chodosh--Daniels-Holgate--Schulze, implies the existence of fattening level set flows starting from smooth embedded closed hypersurfaces. These provide examples related to a question asked by Evans--Spruck. Comment: 23 pages; v2: A new result was added as a corollary thanks to Alec Payne's suggestion; v3: slight modification with references updated
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.15577 Zobrazit plný text záznamu View this record from Arxiv