6 problems

Stability conjecture. The family $\mathcal{B}_\Lambda$ is a stable family of solutions to the Einstein vacuum equations with $\Lambda\geq 0$: the evolution of the small perturbatio…

Let ${\bf g}_{M,a}$ be a subextremal Kerr metric. Let $(\Sigma_0,g_0,k_0)$ be a suitably small perturbation of its initial data, where $\Sigma_0$ is a 3-dimensional manifold, $g_0$…

Let $(\mathcal{M},\mathbf{g})$ be a regular, stationary (appropriately defined), four-dimensional vacuum black hole solution of the Einstein vacuum equations with positive cosmolog…

Fix Kerr-de Sitter parameters $\mathsf{b}$. Let $R^\alpha H_{\mathrm{b}}^\infty$ and $R^\alpha H_{\mathrm{b}}^d$ denote the indicated weighted b-Sobolev spaces, and suppose that fo…

Let $(\mathcal{M},g)$ be the maximal Cauchy development of sufficiently small perturbations of Kerr–de Sitter data with $n$ black-hole regions, initial topology…

Let $(\mathcal{M},g)$ be the maximal Cauchy development for the Einstein vacuum equations with positive cosmological constant of sufficiently small perturbations of subextremal Ker…