5 problems

In a $3+1$-dimensional spacetime satisfying the Einstein vacuum equations … an apparent horizon is the boundary where outward-directed light rays cannot move outward. Ashtekar's ap…

Let $(M^3,g,k)$ be complete Cauchy data satisfying $\mu\ge |J|$, Schwarzschild at infinity with total mass $m$ in a chosen end. Let $\Sigma^2=\partial U^3\in\mathcal S$ be a strict…

Let $(M^n,g,k)$ be complete asymptotically flat Cauchy data with $3\le n\le 7$, and let $\Sigma^{n-1}$ be a generalized trapped surface. Ilmanen's conjecture. There exists a unique…

Let $(M^3,g,k)$ be complete Cauchy data satisfying the nonnegative energy density condition $4\mu \ge |J|4$, and suppose it is Schwarzschild at infinity with total mass $m$ in a ch…

Let $(M^n,g,p)$ be a complete asymptotically flat initial data set containing a generalized trapped surface, with $2\leq n\leq 7$. A hypersurface $\Sigma^{n-1}\subset M^n$ is calle…