In this talk we will present the article “Geometry and analytic properties of the sliced Wasserstein space”, by Sangmin Park and Dejan Slepčev (2023): the sliced Wasserstein distance (SW) is an useful-for-application variant of the usual Wasserstein distance, based on 1 dimensional projections of the measures taken into account. After a brief introduction that highlights similarities and differences of the two metrics, we will characterise absolutely continuous curves for SW, prove some comparisons of SW with fractional Sobolev norms and discuss the behaviour of gradient flows for potential energies in this metric space.
