Volume distance to hypersurfaces: relation with the Blaschke metric and the shape operator

摘要: In this paper we consider the volume distance from a point to convex hypersurface, which is defined as minimal bounded by hyperplane through and hypersurface. We discuss some of its properties, among them centroid property, says that any section. also give for- mulas for hessian matrix distance. Based on these prove normalized converges affine Blaschke metric, when approximate t he hy- persurface along curve whose points are centroids parallel sections. derivative vol- ume at same curve, bilinear form associated with shape operator hypersur- face. This last result may be regarded geometrical interpretation operator.