McDonald, NR;
(2022)
The fundamental solutions of the curve shortening problem via the Schwarz function.
Complex Analysis and its Synergies
, 8
, Article 5. 10.1007/s40627-022-00093-4.
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Abstract
Curve shortening in the z-plane in which, at a given point on the curve, the normal velocity of the curve is equal to the curvature, is shown to satisfy S_{t}S_{z} = S_{zz}, where S(z, t) is the Schwarz function of the curve. This equation is shown to have a parametric solution from which the known explicit solutions for curve shortening flow; the circle, grim reaper, paperclip and hairclip, can be recovered.
| Type: | Article |
|---|---|
| Title: | The fundamental solutions of the curve shortening problem via the Schwarz function |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s40627-022-00093-4 |
| Publisher version: | https://doi.org/10.1007/s40627-022-00093-4 |
| Language: | English |
| Additional information: | © 2022 Springer Nature Switzerland AG. This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Curve shortening, Schwarz function |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10141987 |
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