2 problems

Gromov's quantitative scalar-curvature conjecture. There exist constants $C(g_0)$ and $\varepsilon_0(g_0)$ such that, whenever $\varepsilon\leq \varepsilon_0$, one has

Let $B$ be the unit ball in $\mathbb{R}^n$, and let $g$ and $g_0$ be smooth metrics on $B$. Write $R_g$ for the scalar curvature of $g$ and $\|g-g_0\|_{C^0(B)}$ for their $C^0$ dis…