2 problems

For $d\ge 3$, consider the mass-critical Hartree equation $i\partial_t u+\Delta u=\mu\bigl(|x|^{-2}*|u|^2\bigr)u$ on $\mathbb{R}^d$, with $u(0)=u_0\in L^2(\mathbb{R}^d)$ and…

Let $M$ be a complete Riemannian manifold satisfying the geometric hypotheses in Holopainen’s conjecture. Is every nonnegative $p$-harmonic function $v$ on $M$ such that…