On an area-preserving inverse curvature flow for plane curves

In this paper, we study a $1\mathrm{/}{\kappa }^n$-type area-preserving non-local flow of convex closed plane curves for any $n>0$. We show that the flow exists globally, the length of evolving curve is non-increasing, and the limiting curve will be a circle in the $C^{\mathrm{\infty }}$ metric as time $t\to \mathrm{\infty }$.