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

2018/11/27 by Kohei Nakamura, Nakamura, Kohei
Mathematics · #35B40 #35K55 #53A04 #53C44 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35K55 #msc:53A04 #msc:53C44

paper · pdf · doi:10.48550/arxiv.1811.11576

13 pages. arXiv admin note: text overlap with arXiv:1811.10164

arxiv created 2018/11/27 · arxiv updated 2018/11/29

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.

Citations

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

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