Anisotropic extrinsic radius pinching for hypersurfaces and the stability of the Wulff shape

Abstract

We prove the Hasanis--Koutroufiotis type inequality for the anisotropic extrinsic radius of hypersurfaces in Euclidean space involving the anisotropic mean curvatures. We also study the equality case and proved that an almost extremal hypersurface must be close to the Wulff shape in the sense of the Hausdorff distance.