9 problems

Let … be a non-collapsed sequence of closed Riemannian manifolds with $\mathrm{Ric}\ge -(n-1)$, converging in the Gromov–Hausdorff sense to a compact Ricci limit space $X^n$. Let…

Let $(X^4,\mathsf{d})$ be a noncollapsed Ricci limit space, and consider the set of points whose tangent-cone cross-sections are not homeomorphic to $S^3$. Discrete singularity con…

Let $(X,\mathsf{d})$ be the metric limit under consideration, let $k=\dim_{\mathcal{H}}(X,\mathsf{d})$, and let $\mathcal{H}^k$ denote its $k$-dimensional Hausdorff measure. For…

Let $(X,\mathsf{d},x,\mathfrak{m})$ be a collapsed Ricci limit space of Hausdorff dimension $k$, with its limit measure satisfying … for some $b,k\in(0,\infty)$. Collapsed Ricci li…

Let $X$ be a noncollapsed Ricci limit space of dimension $n$, with singular set ${{\cal S}}$. For each $k\in\{0,\ldots,n-1\}$, let ${{\cal S}}_k$ be the subset of ${{\cal S}}$ cons…

Homeomorphism-type conjecture.

Nonuniqueness-locus conjecture.

The cut-off covering spectrum conjecture. Theorem 7, namely the corresponding cut-off covering spectrum conclusion established earlier in the paper, holds for such limit spaces $X$…

The flat normal bundle conjecture. If $X$ is a limit space as above, then either $X$ has the loops to infinity property or it has a split double cover and it is the flat normal bun…