ON THE GEOMETRIC PROPERTIES OF THE MINKOWSKI OPERATOR
Annotatsiya
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 are derived.The method of finding the Minkowski difference of given regular tetrahedrons in the Euclidean space R 3 is explained.Results for finding the Minkowski difference of given n-dimensional cubes in space R n are also presented.At the end of the article, the obtained results are summarized and a geometric method for finding the Minkowski difference of the convex set M and compact set N given in R n is shown.The theory of foliations is applied to find the Minkowski difference of sets.New geometric concepts such as "dense embedding" and "completely dense embedding" are introduced.An important geometric property of the Minkowski operator is introduced and proved as a theorem.