2 problems

Let $(M^{n},g)$ be a smooth compact Riemannian manifold with boundary $\Sigma$, with $\operatorname{Ric}\geq 0$ and principal curvature tensor $\Pi\geq 1$ on $\Sigma$. Let…

Uniqueness conjecture. If $1<q<n/(n-2)$ and $0<a\leq 1/(q-1)$, then $u$ is constant.