Speaker
Zakaria Fattah
Description
The classical isoperimetric inequality gives a sharp lower bound on the perimeter of a domain with fixed volume, with equality attained by the ball. Reverse isoperimetric inequalities ask the opposite question: how large can the perimeter or surface area be under a volume constraint? Since this problem is generally ill-posed without additional assumptions, one has to impose geometric constraints such as convexity, inclusion, or curvature bounds.
In this talk, we will discuss reverse isoperimetric inequalities under different geometric constraints. Particular attention will be given to the class of convex bodies with prescribed bounds on the radius of curvature