Une relation entre diamètre extrinsèque, intégrale de la courbure de Gauss et inradius pour les hypersurfaces localement convexes d'un espace euclidien. (A relation between external diameter, Gaussian curvature integral and inradius for locally convex hypersurfaces of a Euclidean space)
For locally convex hypersurfaces (with boundary) in Euclidean n-space it is shown that the spherical image contains a half-sphere if \(r\geq \sqrt{2}d\) where r is the intrinsic inradius and d the extrinsic diameter.
scientific article; zbMATH DE number 4054521