Pure Math Colloquium

Kateryna Tatarko, University of Waterloo

Isoperimetric problem: from classical to reverse

The well-known classical isoperimetric problem states that the Euclidean ball has the largest volume among all convex bodies in R^n of a fixed surface area. We will discuss the question of reversing this result for the special class of convex bodies which are intersections of (finitely or infinitely many) balls of radius 1/lambda for some lambda>0. In particular, we will discuss the problem of determining which bodies in this class minimize the volume for a prescribed surface area and completely resolve it in R^3.

MC 5501