Special Configurations of Planes Associated with Convex Compacta

Abstract: Several combinatorial geometry properties of convex compact sets are proved by topological methods. It is proved that if K .sub.1,... ,K .sub.n-1 are convex compacta in R.sup.n , then there is an (n-2)-plane E.sup.n such that for each i=1,2,... ,n-1 there exist three (two orthogonal) hyperplanes containing E and dividing .sub.Ki into six (four) parts of equal volume. It is also proved that for every two bounded continuous distributions of masses in R.sup.3 centrally symmetric with respect to the origin there are three planes dividing both masses into eight equal parts. Bibliography: 9 titles. Article History: Registration Date: 20/10/2004