A fourth-order area-preserving curve flow in centro-equiaffine geometry
Differential Geometry
2026-04-17 v1
Abstract
In this paper, inspired by the work of Guan and Li (2015), we introduce a fourth-order centro-equiaffine invariant curve flow via the affine Minkowski formula. Without any smallness assumptions on the initial curve, we establish the long-time existence of the flow and prove that, as , the evolving curve preserves its enclosed area and converges smoothly to a round circle up to the action of .
Cite
@article{arxiv.2604.14804,
title = {A fourth-order area-preserving curve flow in centro-equiaffine geometry},
author = {Xinjie Jiang and Shengliang Pan and Yanlong Zhang},
journal= {arXiv preprint arXiv:2604.14804},
year = {2026}
}