2 problems

Let $\Omega$ be an open Riemann surface admitting a nontrivial Green function $G_\Omega$, let $u$ be harmonic on $\Omega$, and set $\rho=e^{-2u}$. Define $B_{\Omega,\rho}$ from an…

Let $V$ be a matrix-valued potential and let $Q(x,\ell)$ denote the cube centered at $x$ with side length $\ell$. Let $\mathcal{N}_\gamma(Q(x,\ell))$ be the class of negligible set…