4 problems

Self-consistent initial-data conjecture. Self-consistent initial data for the fourth-order time derivatives of the metric can be obtained from these classical initial data by solvi…

Let $\mathcal C$ be a 3-manifold with $\hbar$-dependent initial metric $g^{\rm in}_{ij}$ and extrinsic curvature $K^{\rm in}_{ij}$, and let $\omega_{\mathcal C}$ be an $\hbar$-depe…

Let $\mathcal C$ be a 3-manifold with classical initial data $(g^{\rm in}_{ij},\dot g^{\rm in}_{ij},g^{(2)\,\rm in}_{ij},g^{(3)\,\rm in}_{ij})$, or…

Let $\mathcal C$ be an initial surface, let $\omega_{\mathcal C}$ be an initial state, and let $g^{(r)}$ denote the $r$th time derivative of the metric on $\mathcal C$. Semiclassic…