An application of interpolation inequalities between the deviation of curvature and the isoperimetric ratio to the length-preserving flow

Kohei Nakamura

doi:10.3934/dcdss.2020385

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2021, Volume 14, Issue 3: 1093-1102. Doi: 10.3934/dcdss.2020385

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An application of interpolation inequalities between the deviation of curvature and the isoperimetric ratio to the length-preserving flow

Kohei Nakamura

Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama City, Saitama 338-8570, Japan

Received: December 31, 2018

Revised: January 31, 2020

Early access: June 2020

Published: March 2021

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Abstract

In recent work of Nagasawa and the author, new interpolation inequalities between the deviation of curvature and the isoperimetric ratio were proved. In this paper, we apply such estimates to investigate the large-time behavior of the length-preserving flow of closed plane curves without a convexity assumption.

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Mathematics Subject Classification: Primary: 53A04, 53E10, 35B40, 35K55.

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References

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