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Research Article | Open Access

Convergence for global curve diffusion flows

University of Wollongong, Wollongong, NSW 2522, Australia
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Abstract

In this note we establish exponentially fast smooth convergence for global curve diffusion flows, and discuss open problems relating embeddedness to global existence (Giga's conjecture) and the shape of Type I singularities (Chou's conjecture).

Keywords

curve diffusionsurface diffusionglobal existenceconvergencecurvaturepartial differential equationgeometric analysis

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Mathematics in Engineering
Volume 4 Issue 1,
February 2022
Pages 1-13
DOI: 10.3934/mine.2022001

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Cite this article:
Wheeler G. Convergence for global curve diffusion flows. Mathematics in Engineering, 2022, 4(1): 1-13. https://doi.org/10.3934/mine.2022001

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Received: 14 April 2020
Accepted: 12 February 2021
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)