A nonlocal curve flow in centro-affine geometry
Differential Geometry
2023-02-28 v1
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.
Cite
@article{arxiv.2207.06627,
title = {A nonlocal curve flow in centro-affine geometry},
author = {Xinjie Jiang and Yun Yang and Yanhua Yu},
journal= {arXiv preprint arXiv:2207.06627},
year = {2023}
}