On the Isoperimetric Inequality and Surface Diffusion Flow for Multiply Winding Curves

Tatsuya Miura, Shinya Okabe

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we establish a general form of the isoperimetric inequality for immersed closed curves (possibly non-convex) in the plane under rotational symmetry. As an application, we obtain a global existence result for the surface diffusion flow, providing that an initial curve is H2-close to a multiply covered circle and is sufficiently rotationally symmetric.

Original languageEnglish
Pages (from-to)1111-1129
Number of pages19
JournalArchive for Rational Mechanics and Analysis
Volume239
Issue number2
DOIs
Publication statusPublished - 2021 Feb

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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