Abstract
In this paper, we investigate the long-term behavior for 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. In addition, we obtain the isoperimetric inequality in centro-affine plane geometry.
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