2 problems

Let $(\Omega^n,\Sigma^{n-1})$ be a compact manifold with boundary, and let $\gamma$ be a metric on $\Sigma$. Ignoring the prescribed mean curvature, a metric $g$ on $\Omega$ induce…

Let $(\Sigma^{n-1},\gamma)$ be a closed Riemannian manifold. A function $\eta$ on $\Sigma^{n-1}$ is the prescribed boundary mean curvature of a compact nonnegative scalar curvature…