5 problems

Let $(M,g)$ be a compact Riemann surface with volume $1$, let $u_k$ be a sequence of blow-up solutions of the mean field equation with $S=\emptyset$, and let $\mathcal{B}$ be its f…

Consider blow-up solutions to the $L^2$-critical nonlinear Schrödinger equation. Let $Q$ denote the ground state, and let $\|Q\|_{L^2}^2$ be its squared $L^2$ mass. Mass quantizati…

Consider a general blow-up solution to the $L^2$-critical nonlinear Schrödinger equation, with singularities and a remaining part away from those singularities. Mass quantization c…

Consider a blow-up solution of the nonlinear Schrödinger equation with singularities, and let $m_k$ be the mass concentrated at the $k$-th singularity, with $m_k\geq \|Q\|_{L^2}^2$…

Brézis–Merle mass quantisation conjecture. Under some mild regularity assumptions on the functions $V_n$ in Theorem A, all the numbers $alpha_p$ are positive integers.