4 problems

Let $N\geqslant 2$ and let $\rho=\mathbf{1}_{[-N/2,N/2]}$. Define … where the intervals are the equal subintervals used in the source. The measure $\mathbb{P}_N$ is an optimal tran…

Let $\rho\in L^1(\mathbb{R}^d,\mathbb{R}_+)$ have total mass $N\geqslant 2$, and suppose that its support is all of $\mathbb{R}^d$. Let $v$ be the SCE potential, that is, a Kantoro…

Let $\rho\in L^1(\mathbb{R}^d,\mathbb{R}_+)$ have mass $N\geqslant 2$, and let $v$ be a Kantorovich potential for the multimarginal optimal transport problem with Coulomb cost … Th…

Let $\mathcal V_{N,\partial}^{(0)}$ and $\mathcal V_{N+1,\partial}^{(0)}$ be the boundary spaces of potentials for the $N$- and $(N+1)$-particle ground-state energies, and let the…