Inequalities for hyperplane sections of convex bodies

Carla Peri

Universita' Cattolica del Sacro Cuore di Milano

Abstract. The problem of finding sections of convex bodies

with minimal or maximal volume has attracted much attention

in convex geometry. There is also a connection to the

slicing problem which is considered the most

unsettled question in the local theory of Banach spaces. I

survey the classical results and present

some recent achievements.