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# Communications in Analysis and Geometry

## Volume 21 (2013)

### Number 3

### Volume preserving centro-affine normal flows

Pages: 671 – 685

DOI: http://dx.doi.org/10.4310/CAG.2013.v21.n3.a9

#### Authors

#### Abstract

We study the long time behavior of the volume preserving $p$-flow in $\mathbb{R}^{n+1}$ for $1\leq p<\frac{n+1}{n-1}$. 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 $C^{\infty}$ topology, modulo the group of special linear transformations.