6 problems

Let $b\Sigma,\stackrel{\circ}{g},K,E_i,B_i,\stackrel{\circ}{\phi},\phi'\d$ be a complete asymptotically flat initial data set for the Einstein–Maxwell–scalar field system, with asy…

Let $\{\mathscr{I},\bm{\gamma},\bm\ell,\ell^{(2)},\sigma,\mathfrak q\}$ be $\mathscr{I}$-structure data of odd dimension $\mathfrak n\ge 7$ admitting a cross-section…

Metric regularity conjecture. The metric regularity condition in Eq. $$ need not be assumed: it should follow from the regularity of the Weyl curvature in combination with a suitab…

Trial projection conjecture. The solution of the first equation of the master system is the map $\pi_{\mathrm{trial}}$ defined by

Consider the perturbative analysis of the wave equation with nonlinearity $r^{-2}|\mathring{\slashed{\nabla}}\phi|^2$, and let the initial data be supported on a fixed spherical ha…

Let the Einstein vacuum equations be posed as a scattering problem with conformally regular data on an ingoing null hypersurface and no incoming radiation from past null infinity.…