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An application of interpolation inequalities between the deviation of curvature and the isoperimetric ratio to the length-preserving flow. (English) Zbl 1466.53005

Summary: 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.

MSC:

53A04 Curves in Euclidean and related spaces
53E10 Flows related to mean curvature
35B40 Asymptotic behavior of solutions to PDEs
35K55 Nonlinear parabolic equations
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References:

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