2 problems

Marques–Neves–Schoen conjecture. There exists $C>0$ such that, for all such hypersurfaces $\Sigma$, one has

Let $u:\Sigma^2\to N^3$ be a branched CMC $h$-immersion, where $N^3$ has strictly positive sectional curvature, and let $g$ denote the genus of $\Sigma$. Write $i_{\mathcal{A}_h}$…