Interpolation inequalities between the deviation of curvature and the isoperimetric ratio with applications to geometric flows

2018/11/26 by Takeyuki Nagasawa, Nagasawa, Takeyuki, Kohei Nakamura +1 · 3 citations
Mathematics · #35B40 #35K55 #53A04 #53C44 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.AP #msc:35B40 #msc:35K55 #msc:53A04 #msc:53C44

paper · pdf · doi:10.48550/arxiv.1811.10164

27 pages

arxiv created 2018/11/26 · openalex publication_date 2018/11/26 · arxiv updated 2018/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the large-time behavior of some geometric flows of closed plane curves without a convexity assumption.

Cited by

• Efficient manifold evolution algorithm using adaptive B-Spline interpolation
• Large-time behavior of the H^-m-gradient flow of length for closed plane curves
• An application of interpolation inequalities between the deviation of curvature and the isoperimetric ratio to the length-preserving flow

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