Evolving convex curves to constant-width ones by a perimeter-preserving flow

Laiyuan Gao and Shengliang Pan

Vol. 272 (2014), No. 1, 131–145

DOI: 10.2140/pjm.2014.272.131

Abstract

This paper deals with a curve evolution problem which, if the curvature of the initial convex curve satisfies a certain pinching condition, keeps the convexity and preserves the perimeter, while increasing the enclosed area of the evolving curve, and which leads to a limiting curve of constant width. In particular, under this flow the limiting curve is a circle if and only if the initial convex curve is centrosymmetric.

Keywords

convex curves, curves of constant width, perimeter-preserving curve flow

Mathematical Subject Classification 2010

Primary: 35K15, 35K55, 53A04

Milestones

Received: 1 September 2013

Revised: 22 December 2013

Accepted: 31 January 2014

Published: 9 October 2014