4 problems

Let $(M^n,g)$ be a complete Riemannian manifold with uniformly positive scalar curvature … Here $\operatorname{width}_{n-2}(M)$ denotes the $(n-2)$-dimensional Uryson width. Gromov…

Gromov's conjecture. There should exist a continuous self-map $R:X\to X$ such that $R(X)$ has topological dimension $n-2$ and

Let $X$ be a compact, or even proper, metric space. Say that $X$ has locally small $n$-Hausdorff content when every point has a neighborhood with sufficiently small $n$-dimensional…

Let $m$ and $k$ be as in the claim, let $1\leq c\leq m$, and let $g_0$ denote the unit sphere metric on $S^m$. For a metric $g$ on $S^m$, write $\Lambda^k g\leq\Lambda^k g_0$ for t…