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Geometric Flows

Ed. by Carfora, Mauro / Mantegazza, Carlo

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2353-3382
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The area preserving curve shortening flow with Neumann free boundary conditions

Elena Mäder-Baumdicker
  • Corresponding author
  • Karlsruhe Institute of Technology, Department of Mathematics, Englerstr. 2, D-76131 Karlsruhe, Germany
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Published Online: 2015-05-25 | DOI: https://doi.org/10.1515/geofl-2015-0004

Abstract

We study the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain in the Euclidean plane. Under certain conditions on the initial curve the flow does not develop any singularity, and it subconverges smoothly to an arc of a circle sitting outside of the given fixed domain and enclosing the same area as the initial curve.

Keywords: Geometric analysis; Curve shortening flow; Free boundary; Neumann boundary condition; Singularities; Volume preserving

MSC: 58J32; 35K93; 35K65; 35K59

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About the article

Received: 2015-02-02

Accepted: 2015-02-23

Published Online: 2015-05-25


Citation Information: Geometric Flows, Volume 1, Issue 1, ISSN (Online) 2353-3382, DOI: https://doi.org/10.1515/geofl-2015-0004.

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© 2015 Elena Mäder-Baumdicker. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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