2 problems

Let $B\subset\mathbb{R}^n$ be a unit ball, with $n\geq 3$, and let $u$ be harmonic in $4B$, vanish at the center of $B$, have stable growth in $B$, and satisfy…

Let $M$ be a closed surface covered by approximately $\lambda$ geodesic discs $B_i$ of radius $C/\sqrt{\lambda}$, with every point covered at most $C_1$ times and with the Laplace…