Title: Upper bounds for the perimeter plane of convex bodies

Speaker: Dr. Alexey Glazyrin

Date: Friday, February 15

Place: LHSB 2.310

Time: 2:00PM

**ABSTRACT**

It is well known that if C and D are two plane convex bodies such that C is inside D, then the perimeter of C is not greater than the perimeter of D. In other words, the maximum perimeter of a convex body lying inside a given convex body D is equal to the perimeter of D. In this talk we are interested in answering the following more general question:

For a given natural k, what is the maximum total perimeter of k convex bodies with disjoint interiors lying inside a given convex body D?

We answer this question in the case when D is a square or an arbitrary triangle. A weaker bound is obtained for general plane convex bodies.