4 problems

$L_{\infty}$-algebra conjecture. There exists an $L_{\infty}$ structure on the complex $({\bf F}^{\bullet}_{{\bf b}^-},\mathcal{Q})$, such that its bilinear operation is the symmet…

Let $V\subset M$ be a precompact open set. For sufficiently small $\epsilon>0$, let $g_\epsilon$ be the formal solution on $M_\epsilon$ obtained by gluing small Kerr black holes al…

Let $(\mathcal{M},g)$ be an asymptotically flat solution of the Einstein vacuum equations … An event horizon is the boundary separating the region from which observers can reach in…

Let $(\Sigma,q,K)$ be asymptotically flat Cauchy data for the $3+1$-dimensional vacuum Einstein equations admitting a spacelike translational Killing field, and let its maximal Cau…