7 problems

A space-periodic vacuum configuration is a regular static vacuum spacetime whose geometry repeats periodically along an axis, as in the Myers–Korotkin–Nicolai solutions. Myers's co…

ALE hyperkähler conjecture. Any ALE Ricci-flat $4$-manifold must be hyperkähler.

A Ricci-flat four-manifold is a closed four-dimensional manifold equipped with a Ricci-flat Riemannian metric. Covering conjecture. Every closed Ricci-flat four-manifold should be…

Half-conformal-flatness conjecture. Every Ricci-flat ALE $4$-manifold is half-conformally flat; with the appropriate orientation, this means

A Ricci-flat spin manifold is a smooth manifold $F$ with a Ricci-flat Riemannian metric and a spin structure. Finite-cover parallel-spinor conjecture. Every Ricci-flat spin manifol…

A compact Ricci-flat manifold is a compact manifold equipped with a Ricci-flat Riemannian metric, where the metric is considered up to multiplication by a positive constant. A targ…

Let $M^n$ be a Ricci-flat manifold, and let $alpha$ be the exponent appearing in Corollary. Quadratic curvature blow-up conjecture. $alpha$ in Corollary can be chosen to be $1$. A…