arXiv subjects

Francesco Maggi

Publications and source records attributed to Francesco Maggi.

39 records · Page 3Linked to original sources

arXiv2013

Rigidity of equality cases in Steiner's perimeter inequality

Characterization results for equality cases and for rigidity of equality cases in Steiner's perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner's symmetral under consideration.) We achieve this through the introduction of a suitable measure-theoretic notion of connectedness and a fine analysis of barycenter functions for sets of finite perimeter having segments as orthogonal sections with respect to an hyperplane.

math.AP↗

arXiv2013

Essential connectedness and the rigidity problem for Gaussian symmetrization

We provide a geometric characterization of rigidity of equality cases in Ehrhard's symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic notion of connectedness for Borel sets, inspired by Federer's definition of indecomposable current.

math.AP↗

arXiv2011

Quantitative stability in the isodiametric inequality via the isoperimetric inequality

The isodiametric inequality is derived from the isoperimetric inequality trough a variational principle, establishing that balls maximize the perimeter among convex sets with fixed diameter. This principle brings also quantitative improvements to the isodiametric inequality, shown to be sharp by explicit nearly optimal sets.

math.MG↗