An inequality for the minimum affine curvature of a plane curve
In the paper the following inequality for the minimum affine curvature \(\mu_\text{min}\) of a planar smooth simple closed curve \(\gamma\) is given: \[\mu_\text{min}\leq(\pi/A)^{2/3},\] where \(A\) is the enclosed area of \(\gamma\). The inequality is obtained as an application of the affine curve shortening flow and the affine isoperimetric inequality \[\mathcal L^3\leq 8\pi^2A\] for a closed convex curve \(\gamma\), where \(\mathcal L\) and \(A\) are the affine length and the enclosed area of \(\gamma\), respectively.
scientific article; zbMATH DE number 7226769
scientific article