Tutte Colloquium | Kateryna Tatarko, The reverse isoperimetric problem for intersections of balls

Abstract: The classical isoperimetric problem states that the Euclidean ball has the largest volume among all convex bodies of a fixed surface area. What if we ask for the smallest volume instead? Without additional constraints, the volume can be arbitrarily small. We will discuss this reverse question for the intersections of balls of fixed radius, the class of convex bodies for which the question becomes meaningful. In particular, we will show that a lens, the intersection of two balls, minimizes the volume for a prescribed surface area in this class.