Restrictions of Inequality Type on the Values of the Mixed Volumes of Tuples of Convex Bodies

Student: Smirnova Iuliia

Supervisor: Alexander Isaakovich Esterov

Educational Programme: Joint Bachelor's Programme with the Centre for Teaching Excellence (Bachelor)

Year of Graduation: 2021

In this paper, we will talk about convex bodies. To begin with, we introduce the basic concepts of convex geometry, on which the rest of the work is based. Using the knowledge gained from writing last year's course paper, we are moving deeper into the theory of convex sets. In this regard, the works of Rudolf Heine are interesting, in which all possible restrictions of the type of inequalities on the mixed areas of pairs and threes of convex bodies on the plane are found, and it is shown that for a larger number of bodies this set of inequalities is not complete. His methods remain original and insufficiently known to modern mathematicians.

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