6 problems

Let $\psi^{\mathrm{dat}}$ be data as in the paper's scattering-data definition, with $d>0$ and $N>5$, for the linearised equation on the hypersurface $\Sigma_1$. Let…

Decay conjecture in the hyperbolic case.

Decay conjecture in the flat case.

Let $\mathcal{H}^+$ be the event horizon and let $v$ be the standard advanced time null coordinate. Massive scalar-field tail conjecture. For smooth, regular, generic admissible da…

Charged massless scalar decay conjecture. For smooth, regular, generic admissible data with a non-empty black hole and $m^2=0$,

Hod–Piran conjecture. Among all admissible, sufficiently regular and decaying data, there exists a generic subclass such that, whenever the maximal future development satisfies…