4 papers
-geodesic convexity of the squared sliced-Wasserstein distance
Giacomo Cozzi, Filippo Santambrogio
The squared Wasserstein distance with respect to a fixed target measure is not a convex function along Wasserstein geodesics over when . Still, in dimension…
Stability of the ball in isoperimetric inequalities between two fractional perimeters
G. Alberti, G. Cozzi, A. Massaccesi +1
We consider the isoperimetric inequality involving the -perimeter and the -perimeter with , and show that the ball is a local minimizer of the (scale-invariant) isop…
Uniform small energy regularity for fractional geometric problems
Marco Badran, Giacomo Cozzi
We prove small energy regularity for a parabolic boundary reaction Ginzburg-Landau problem in the full range , answering a question posed by Hyder, Segatti, Sire and Wa…
Long-Time Asymptotics of the Sliced-Wasserstein Flow
Giacomo Cozzi, Filippo Santambogio
The sliced-Wasserstein flow is an evolution equation where a probability density evolves in time, advected by a velocity field computed as the average among directions in the unit…