Communications in Analysis and Geometry

Volume 21 (2013)

Number 3

Volume preserving centro-affine normal flows

Pages: 671 – 685

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

Authors

Mohammad N. Ivaki (Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, Canada)

Alina Stancu (Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, Canada)

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.

Published 5 July 2013