Narrow Results

The aim of this paper is to present a convex curve evolution problem which is determined by both local (curvature $\kappa$) and global (area $A$) geometric quantities of the evolving curve. This flow will decrease the perimeter and the area of the evolving curve and make the curve more and more circular during the evolution process. And finally, as $t$ goes to infinity, the limiting curve will be a finite circle in the $C^{\infty }$ metric.

We prove that the Borromean Rings are the only Brunnian link of 3 or 4 components that can be built out of convex curves.