4 problems

Let $(\Sigma,g,k)$ be vacuum initial data that are asymptotically flat, and consider localization to a cone as in the Carlotto–Schoen construction. Carlotto's conjecture. Such loca…

Let $(M,g,K) fin \mathcal{M}_{\textnormal{AF}}$ and let $\{\Sigma_r\}_{r\in[r_0,\infty)}\subset\mathcal{M}$, where … Suppose that the inner boundary $\Sigma_{r_0}$ is a generalized…

Modified no-KIDs conjecture. Under this modified hypothesis, the results of Corvino and Huang should apply in the argument of Chruściel and Galloway, allowing one to remove the con…

Let $M_{\scriptscriptstyle ADM}$ be the total ADM mass of an asymptotically flat initial data slice, and let $S_{out}$ be its outermost generalized apparent horizon. Write…