57 citations · 413 across the 51 of their papers we have counts for
3 papers · 1 filter
Obstructions to regularity in the classical Monge problem
Maria Colombo, Emanuel Indrei
We provide counterexamples to regularity of optimal maps in the classical Monge problem under various assumptions on the initial data. Our construction is based on a variant of the…
Rigidity of equality cases in Steiner's perimeter inequality
Filippo Cagnetti, Maria Colombo, Guido De Philippis +1
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 equalit…
Essential connectedness and the rigidity problem for Gaussian symmetrization
Filippo Cagnetti, Maria Colombo, Guido De Philippis +1
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…