An estimate for the anisotropic maximum curvature in the planar case

Abstract

We fix a Finsler norm F and, using the anisotropic curvature flow, we prove that in the plane the anisotropic maximum curvature \(k^F_{\max }\) of a smooth Jordan curve is such that \( k^F_{\max }(\gamma )\ge \sqrt{\kappa /A}\), where A is the area enclosed by \(\gamma \) and \(\kappa \) the area of the unitary Wulff shape associated to the anisotropy F.