arXiv subjects
Publications and source records attributed to Toshimi Inoue.
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.
In the paper, we study the Gauss map of a completely immersed anisotropic minimal surface with respect to convex parametric integrand in $\mathbb{R}^3$. By a local analysis, we prove the discreteness of the critical set of the Gauss map of an anisotropic minimal surface. In particular, we may consider the Gauss map as a branched covering map from an anisotropic minimal surface to the unit sphere. As a consequence, we may obtain an upper and a lower estimate for the Morse index of an anisotropic minimal surface by applying some conformal geometric technics to the Gauss map.