6 problems

Schwarzschild Cauchy data are Cauchy data induced by a Schwarzschild spacetime. An axially symmetric deformation preserves axial symmetry, and a maximal development is the maximal…

Malec–O Murchadha conjecture. Given any constant mean curvature $H$, the Kruskal extension can be foliated by the TSS-CMC hypersurfaces $\{\Sigma_H\}$. The paper presents this as t…

Malec–O Murchadha conjecture. The TSS-CMC hypersurfaces in $\Sigma^+_{H,-8M^3H>c>c_H}$ form a foliation between $\tilde{\Sigma}^-_{H,-8M^3H}$ and the hyperbola $r=r_H$. This is one…

Let the extended Schwarzschild spacetime be the Kruskal extension. A spacelike spherically symmetric constant-mean-curvature (SS-CMC) hypersurface is a spacelike, spherically symme…

Let the extended Schwarzschild spacetime be the Kruskal extension, and let a CMC foliation mean a foliation by complete spacelike hypersurfaces of constant mean curvature, with the…

Let $\Sigma$ be a spacelike $2$-surface in Schwarzschild spacetime, and let $\vec{J}$ denote its dual mean curvature vector. Suppose that the past null hypersurface generated by…