4 problems

The existence conjecture. Every simply connected Riemannian manifold $(M,\mathtt{g})$ with positive (respectively, non-negative) sectional curvature admits a codimension-one singul…

Horizontal diameter rigidity conjecture. For any singular Riemannian foliation on a unit sphere $\mathbb{S}^{n}$, we have

Let $M$ be a closed simply connected Riemannian manifold with non-negative sectional curvature. A singular Riemannian foliation of codimension 1 is a singular Riemannian foliation…

Molino's conjecture. The partition $\overline{\mathcal{F}}$ given by the closures of the leaves of $\mathcal{F}$ is again a singular Riemannian foliation.