Volume preserving centro-affine normal flows

We study the long time behavior of the volume preserving $p$-flow in ${\mathbb{R}}^{n+1}$ for $1\le p<\frac{n+1}{n-1}$. By extending Andrews’ technique for the flow along the affine normal, we prove that every centrally symmetric solution to the volume preserving $p$-flow converges sequentially to the unit ball in the $C^{\mathrm{\infty }}$ topology, modulo the group of special linear transformations.