4 problems

BKL scattering conjecture. Scattering at $\tau to \infty$ from the dynamical system defined by $\mathcal{A}$ to that defined by $\mathcal{E}_\Phi$ defines a smooth map

Bounded $L^2$-curvature conjecture. The Einstein scalar field equations admit local Cauchy developments for initial data sets $(\Sigma,g,k,u_{0},u_{1})$ with locally finite $L^{2}$…

Non-spherical stability conjecture. Spherically symmetric locally BV-scattering dispersive solutions to the Einstein-scalar field equations are stable against non-spherically symme…

Large-data local BV scattering conjecture. There exists initial data of arbitrarily large BV norm whose maximal global development scatters locally in the BV norm.