Solution branching of a general perimeter partition problem.
We establish some Brunn-Minkowski type inequalities for radial Blaschke-Minkowski homomorphisms with respect to Orlicz radial sums and differences of dual quermassintegrals.
* This work was supported by the CNR while the author was visiting the University of Milan.To a convex set in a Banach space we associate a convex function (the separating function), whose subdifferential provides useful information on the nature of the supporting and exposed points of the convex set. These points are shown to be also connected to the solutions of a minimization problem involving the separating function. We investigate some relevant properties of this function and of its conjugate...
The isoperimetric inequality for Steiner symmetrization of any codimension is investigated and the equality cases are characterized. Moreover, a quantitative version of this inequality is proven for convex sets.