Linear combinations of convex hypersurfaces in non-Euclidean geometry

It is the aim of the paper to generalize the Minkowski addition, and more general, the Minkowski linear combination for a pair of convex bodies M 1 and M 2 in the euclidean n-space to non-Euclidean geometry. We succeed in the spherical case for arbitrary spherically convex bodies, whereas in the hyperbolic case the class of hyperbolically convex bodies has to be restricted in a suitable way. Practical computation of these operations for M 1 and M 2 is indicated after representation of their boundaries ∂M 1 and ∂M 2 with the help of certain support functions. © 2011 The Managing Editors.