4 problems

Let $M$ be an isoparametric hypersurface or a focal submanifold of the unit sphere $\mathbb{S}^n$. Tang's conjecture. Every such isoparametric hypersurface and focal submanifold ad…

Let $(N^n,\mathfrak{F})$ be an isoparametric foliation. Suppose its leaves have nonnegative or positive leafwise sectional curvature, $K_{\mathrm{sec}}^F\geqslant0$ or…

Let $M$ be a closed simply connected manifold admitting a Riemannian metric of nonnegative sectional curvature. Grove's conjecture. Then $M$ has a DDBD structure, that is, an isopa…

Let $(N^{n+1},\mathbf{g})$ be a compact Riemannian manifold with boundary $\partial N$, and let $(M_c,\bar{\mathbf{g}}|_{M_c})$ be an isoparametric hypersurface in the unit sphere…