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arXiv · 2604.14804

A fourth-order area-preserving curve flow in centro-equiaffine geometry

Xinjie Jiang·Shengliang Pan·Yanlong Zhang
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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 $t \to +\infty$, the evolving curve preserves its enclosed area and converges smoothly to a round circle up to the action of $\mathrm{SL}(2)$.

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Xinjie Jiang, Shengliang Pan, Yanlong Zhang. 2026-04-16. A fourth-order area-preserving curve flow in centro-equiaffine geometry. https://arxiv.org/abs/2604.14804

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