Nonlocal Flow of Convex Plane Curves and Isoperimetric Inequalities
Differential Geometry
2010-05-05 v1
Abstract
In the first part of the paper we survey some nonlocal flows of convex plane curves ever studied so far and discuss properties of the flows related to enclosed area and length, especially the isoperimetric ratio and the isoperimetric difference. We also study a new nonlocal flow of convex plane curves and discuss its evolution behavior. In the second part of the paper we discuss necessary and sufficient conditions (in terms of the (mixed) isoperimetric ratio or (mixed) isoperimetric difference) for two convex closed curves to be homothetic or parallel.
Keywords
Cite
@article{arxiv.1005.0438,
title = {Nonlocal Flow of Convex Plane Curves and Isoperimetric Inequalities},
author = {Yu-Chu Lin and Dong-Ho Tsai},
journal= {arXiv preprint arXiv:1005.0438},
year = {2010}
}
Comments
23 pages