5 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…

Kerr stability conjecture. The maximal Cauchy development of any initial data set for the Einstein vacuum equations, sufficiently close to a subextremal Kerr initial data set in a…

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, $g_0$…

For Kerr--de Sitter parameters $a$, $\Lambda$, and $M$ satisfying … and lying in the shaded region specified by the source, quasinormal modes are complex frequencies $\lambda$ for…

The spacetime under consideration satisfies the hypotheses of Theorem … is weakly ultimately Schwarzschildean to order $k+2$. This conjecture is motivated by techniques that obtain…