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VOL. 85 | 2020 A note on traveling waves for area-preserving geometric flows
Takashi Kagaya, Yoshihito Kohsaka

Editor(s) Yoshikazu Giga, Nao Hamamuki, Hideo Kubo, Hirotoshi Kuroda, Tohru Ozawa

Abstract

The traveling waves for area-preserving geometric flows will be discussed. For an evolving plane curve, which is governed by the area-preserving curvature flow and has two endpoints moving freely on the $x$-axis with generating constant contact angles, we prove that there exists only a convex traveling wave. In the proof, a boundary value problem for an angle function associated with the Gauss map of the profile curve is analyzed by means of a shooting argument.

Information

Published: 1 January 2020
First available in Project Euclid: 29 December 2020

Digital Object Identifier: 10.2969/aspm/08510227

Subjects:
Primary: 35C07
Secondary: 34B08, 53C44

Rights: Copyright © 2020 Mathematical Society of Japan

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