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Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

Azé, D., Lucchetti, R. (1996)

Serdica Mathematical Journal

* 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...

Stability of the Steiner symmetrization of convex sets

Marco Barchiesi, Filippo Cagnetti, Nicola Fusco (2013)

Journal of the European Mathematical Society

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.

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