For a large class of supermodular integrands, we establish conditions under which balls are the unique (up to translations) maximizers of the Riesz-type functionals with constraints. Source: http://arxiv.org/abs/0903.2821v1

We prove the uniqueness of the maximizers of a Hardy-Littlewood type functional under constraints. We also establish a quantitative stability estimate. Introduction Source: http://arxiv.org/abs/0903.2826v1

We prove the existence of radial and radially decreasing ground states of an m-coupled nonlinear Schrodinger equation with a general nonlinearity. Source: http://arxiv.org/abs/0903.2854v1