Uniqueness and shape of simplex ground states for aggregation--diffusion energies with mild repulsion

Tongseok Lim, Geuntaek Seo

We study global minimizers in ${\mathbb{R}}^d$ of the free energy ${\mathcal{E}}_{\kappa }=\mathcal{W}+\kappa \mathcal{U}$, where $\mathcal{W}$ is a power-law interaction energy with mild repulsion…