5 problems

Let $\rho$ be the energy density and $J$ the momentum density on a smooth, conformally compact, geometrically finite general relativistic initial data set satisfying the energy con…

Let $(M,g,\Sigma)$ be an asymptotically hyperbolic manifold with scalar curvature $R_g$ and boundary mean curvature $H_g$ satisfying … For any admissible chart $F$, let…

Riemannian Horowitz-Myers conjecture. The Wang mass-energy $m$ of $(M,g)$ satisfies $m\ge m_0$, where $m_0$ is the mass of the Horowitz-Myers geon having least mass among all Horow…

Let $(M,g)$ be a complete, $n$-dimensional Riemannian asymptotically hyperbolic manifold whose conformal infinity is the $(n-1)$-unit sphere. Let $R_g$ denote the scalar curvature…

Let $(M,g)$ be an asymptotically hyperbolic $3$-manifold with scalar curvature $R\geq -6$ and mass $M$. Let $\Sigma_0$ be an outermost sphere with mean curvature $H(\Sigma_0)=2$. W…