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On the dynamics of formation of generic singularities of mean curvature flow

Gang, Zhou (2022) On the dynamics of formation of generic singularities of mean curvature flow. Journal of Functional Analysis, 282 (12). Art. No. 109458. ISSN 0022-1236. doi:10.1016/j.jfa.2022.109458. https://resolver.caltech.edu/CaltechAUTHORS:20220309-982420000

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Abstract

We study formation of generic singularities under mean curvature flow by combining the different approaches and results, namely the techniques used by the author and the collaborators, where we obtained detailed information when the initial hypersurfaces are close to cylinders, and these results by Colding and Minicozzi, which included all the generic blowups. Here we choose to study the cases where the rescaled flow converges to the cylinder S¹×R³, and we extend the region controlled by Colding and Minicozzi to find a finer description of a neighborhood of the singularity.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jfa.2022.109458DOIArticle
https://arxiv.org/abs/1708.03484arXivDiscussion Paper
ORCID:
AuthorORCID
Gang, Zhou0000-0002-1649-1823
Additional Information:© 2022 Elsevier Inc. Received 26 July 2021, Accepted 7 February 2022, Available online 9 March 2022. Partly supported by NSF grant DMS-1308985 and DMS-1443225.
Funders:
Funding AgencyGrant Number
NSFDMS-1308985
NSFDMS-1443225
Subject Keywords:Mean curvature flow; Formation; Generic singularity
Issue or Number:12
DOI:10.1016/j.jfa.2022.109458
Record Number:CaltechAUTHORS:20220309-982420000
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20220309-982420000
Official Citation:Zhou Gang, On the dynamics of formation of generic singularities of mean curvature flow, Journal of Functional Analysis, Volume 282, Issue 12, 2022, 109458, ISSN 0022-1236, https://doi.org/10.1016/j.jfa.2022.109458.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:113814
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:09 Mar 2022 23:14
Last Modified:28 Mar 2022 21:25

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