Geometric properties of the Minkowski operator

Abstract

This article is about Minkowski difference of sets, which is one of the Minkowski operators. The necessary and sufficient conditions for the existence of the Minkowski difference of given regular polygons in the plane were derived. The method of finding the Minkowski difference of given regular tetrahedrons in the Euclidean space R³ was explained. At the end of the article, the obtained results were summarized and a geometric method for finding the Minkowski difference of the convex set M and compact set N given in Rⁿ was shown. The theory of foliations was applied to find the Minkowski difference of sets. New geometric concepts such as “dense embedding” and “completely dense embedding” were introduced. An important geometric property of the Minkowski operator was introduced and proved as a theorem.