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 the anisotropic maximum curvature $k_{\max }^F$ of a smooth Jordan curve is such that $k_{\max }^F(\gamma )\ge \sqrt{\kappa /A}$ , where $A$ is the area enclosed by $\gamma$ and $\kappa$ the area of the unitary Wulff shape associated to the anisotropy $F$.