4 problems

Let $(\mathbf{E}_1,\mathbf{P}_1,\mathbf{J}_1)$ and $(\mathbf{E}_2,\mathbf{P}_2,\mathbf{J}_2)$ lie in $\mathbb{R}_+\times\mathbb{R}^3\times\mathbb{R}^3$, with…

Let $(M,g,K)$ be a compact, vacuum initial data set whose evolution is a non-static spacetime. Suppose there is a family of future rays intersecting the initial Cauchy surface in a…

Let $(M,g,K)$ be an initial data set, equipped with the $C^{2,\alpha}$ norm, and let its associated spacetime be the evolution determined by the data. Open-set conjecture. There is…

Non-negativity conjecture. Consider a GB initial data set. Then $\mathcal{M}\left(v,\lambda',Y\right)$ is a non-negative functional for any orbit space.