Existence of free boundary disks with constant mean curvature in ${\mathbb{R}}^3$

Da Rong Cheng

Given a surface $\hat{I}\pounds$ in ${\mathbb{R}}^3$ diffeomorphic to $S^2$, Struwe (Acta Math., 1988) proved that for almost every $H$ below the mean curvature of the smallest sphere enclosing…