4 papers
Rigidity and stability of Caffarelli's log-concave perturbation theorem
Guido De Philippis, Alessio Figalli
In this note we establish some rigidity and stability results for Caffarelli's log-concave perturbation theorem. As an application we show that if a 1-log-concave measure has almos…
Spectral inequalities in quantitative form
Lorenzo Brasco, Guido De Philippis
We review some results about quantitative improvements of sharp inequalities for eigenvalues of the Laplacian.
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…
Sobolev regularity for Monge-Ampère type equations
Guido De Philippis, Alessio Figalli
In this note we prove that, if the cost function satisfies some necessary structural conditions and the densities are bounded away from zero and infinity, then strictly -convex…