A characterization of convex calibrable sets in IRN

The main purpose of this paper is to characterize the calibrability of bounded convex sets in IRN by the mean curvature of its boundary, extending the known analogous result in dimension 2. As a by-product of our analysis we prove that any bounded convex set C of class C-1,C-1 has a convex calibrable set K in its interior, and and for any volume V is an element of [| K|, |C|] the solution of the perimeter minimizing problem with fixed volume V in the class of sets contained in C is a convex set. As a consequence we describe the evolution of convex sets in IRN by the minimizing total variation flow.