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arXiv · 2207.06627

A nonlocal curve flow in centro-affine geometry

Xinjie Jiang·Yun Yang·Yanhua Yu
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Abstract

In this paper, the isoperimetric inequality in centro-affine plane geometry is obtained. We also investigate the long-term behavior of an invariant plane curve flow, whose evolution process can be expressed as a second-order nonlinear parabolic equation with respect to centro-affine curvature. The forward and backward limits in time are discussed, which shows that a closed convex embedded curve may converge to an ellipse when evolving according to this flow.

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Xinjie Jiang, Yun Yang, Yanhua Yu. 2022-07-14. A nonlocal curve flow in centro-affine geometry. https://doi.org/10.1016/j.jfa.2023.109904

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