Daniels-Holgate, J. M. (2022) Approximation of mean curvature flow with generic singularities by smooth flows with surgery. Advances in Mathematics, 410 . 108715. doi:10.1016/j.aim.2022.108715 ISSN 0001-8708.

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Abstract

We construct smooth mean curvature flows with surgery that approximate weak mean curvature flows with only spherical and neck-pinch singularities. This is achieved by combining the recent work of Choi-Haslhofer-Hershkovits, and Choi-Haslhofer-Hershkovits-White, establishing canonical neighbourhoods of such singularities, with suitable barriers to flows with surgery. A limiting argument is then used to control these approximating flows. We conclude by improving the entropy bound on the low-entropy Schoenflies conjecture.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Flows (Differentiable dynamical systems), Geometric analysis
Journal or Publication Title:	Advances in Mathematics
Publisher:	Academic Press
ISSN:	0001-8708
Official Date:	3 December 2022
Dates:	Date Event 3 December 2022 Published 5 October 2022 Available 21 September 2022 Accepted 29 June 2021 Submitted
Volume:	410
Number of Pages:	42
Article Number:	108715
DOI:	10.1016/j.aim.2022.108715
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	25 October 2022
Date of first compliant Open Access:	25 October 2022

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