5 problems

Let $n$ and $q$ be integers with $n\geq 3$ and $1\leq q<n/2$. Let $(M^n,g)$ be asymptotically flat of order $\tau>(n-2q)/(q+1)$, with integrable nonnegative $q$-th Gauss–Bonnet cur…

Let $n$ and $q$ be integers with $n\geq 3$ and $1\leq q<n/2$. Let $(M^n,g)$ be asymptotically flat of order $\tau>(n-2q)/(q+1)$, with integrable nonnegative $q$-th Gauss–Bonnet cur…

Let $k<\frac n2$ and let $\mathcal{M}^n$ be a complete asymptotically hyperbolic manifold of decay order $\tau>\frac{n}{k+1}$ with finite integral … Assume the dominant energy cond…

Let $m_k=m_{GBC}$ be the Gauss-Bonnet-Chern mass, let $\Sigma$ be the relevant horizon boundary, and let $|\Sigma|$ denote its area. Then Gauss-Bonnet-Chern Penrose conjecture. … T…

Let $(M^n,g)$ be an asymptotically flat manifold with decay order … and suppose that its Gauss-Bonnet curvature satisfies $L_2(g)\geq 0$. The Gauss-Bonnet-Chern mass conjecture. Th…