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Interpolation inequalities between the deviation of curvature and the isoperimetric ratio with applications to geometric flows. (English) Zbl 1442.53004
In this paper, several inequalities for the isoperimetric ratio for plane curves are derived. In particular, the authors obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. They also provide applications of their interpolation inequalities to the analysis of the long-time behavior of some geometric flows of closed plane curves.

MSC:
53A04 Curves in Euclidean and related spaces
35B40 Asymptotic behavior of solutions to PDEs
35K55 Nonlinear parabolic equations
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Full Text: Euclid