Discrete isoperimetric problems in spaces of constant curvature
Discrete isoperimetric problems in spaces of constant curvature
Abstract The aim of this paper is to prove isoperimetric inequalities for simplices and polytopes with vertices in Euclidean, spherical and hyperbolic d ‐space. In particular, we find the minimal volume d ‐dimensional hyperbolic simplices and spherical tetrahedra of a given inradius. Furthermore, we investigate the properties of maximal volume …