ON MOTHER BODIES OF CONVEX POLYHEDRA

Abstract

If › is a bounded domain in R N provided with a mass distribution › (e.g., Lebesgue measure restricted to ›), another mass distribution sitting in › and producing the same external Newtonian potential as › is sometimes called a mother body of ›, provided it is maximally con- centrated in some sense. We rst discuss the meaning of this and formulate ve desirable properties (\axioms) of mother bodies. Then we show that convex polyhedra do have unique mother bodies in that sense made precise in the case that › is either Lebesgue measure on ›, hypersurface measure on @›, or any mixture of these two.