2 problems

Let $n\geq 2$ be an integer, let $E\subset \mathbb{R}^n$ have boundary $\Sigma:=\partial E$ of class $C^2$, and let $\Omega\subset \mathbb{R}^n$ be open. For $\lambda>0$, define ……

Let $M^n$ be a compact hypersurface of genus $0$ in $\mathbb{R}^{n+1}$ whose volume equals that of the unit sphere, and let $\mathcal{W}(M)$ denote its Willmore functional. Willmor…