**DOI: ****10.12732/ijam.v37i2.4
**

** **

**ON THE GEOMETRIC PROPERTIES**

**OF THE MINKOWSKI OPERATOR**

** **

**Mashrabjon Mamatov 1** **, Jalolxon
Nuritdinov 2 , **

** **

1 Department of Geometry and Topology

of National University of Uzbekistan

Tashkent - 100174, UZBEKISTAN

2 Department of Digital Technologies and

Mathematics of Kokand University

Kokand - 150700, UZBEKISTAN

**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 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.

**How
to cite this paper?**

**DOI: 10.12732/ijam.v3****7****i2.4
Source: **International Journal of Applied Mathematics

**References**

** **

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