3 problems

Let $M_{p,q}=\mathbf S^p\times\mathbf S^q\times[-1,1]$ be a Clifford band, and let $g$ be a smooth metric on $M_{p,q}$. Clifford-band width conjecture. If … then … This is a propos…

Let $M$ be a simply connected Einstein four-manifold with positive scalar curvature and non-negative sectional curvature. Folklore conjecture. The manifold must be one of the follo…

Let $(M,g)$ be a smooth four-dimensional Einstein manifold satisfying … for a constant $\lambda>0$, and suppose that its sectional curvature is non-negative. The metrics $g_0$,…