Sharp Stability for the Interaction Energy

This paper is devoted to stability estimates for the interaction energy with radially symmetric potentials that are strictly decreasing in radial variable, such as Coulomb and Riesz potentials. For a general density function, we first prove estimate terms of $$L^1$$ asymmetry density, extending some previous results by Burchard–Chambers (Calc Var PDE 54(3):3241–3250, 2015; A result higher dimensions. arXiv:2007.11664 , 2020). Frank–Lieb (Ann Sc Norm Super Pisa Cl Sci XXII:1241–1263, 2021) Fusco–Pratelli (ESAIM Control Optim Calcul 26:113, 2020) characteristic functions. We also obtain 2-Wasserstein distance between its rearrangement. Finally, consider special case Newtonian potential, address conjecture Guo on energy.