4 problems

Let $(M,g)$ be a Riemannian manifold and let ${\mathcal{F}}$ be a singular Riemannian foliation on $M$. Consider the partition $\overline{{\mathcal{F}}}$ of $M$ by the closures of…

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…