4 problems

Let $\mathcal{C}$ be a compact family of closed cones. Suppose that at each point of a set $S$, each blow-up of $S$ is contained in some element of $\mathcal{C}$. Let $d$ be the la…

Let $C$ be a closed cone in $\mathbb{R}^n$. Its building dimension is … where $\operatorname{diff}(S):=\{x-y:x,y\in S\}$. White's building-dimension conjecture. The building dimens…

Let $\mathcal{C}$ denote the cone. Let $S$ be either the group $\mathcal{C}_2$ representing a two-fold rotation about an axis perpendicular to the $z$-axis, or the group…

Let $C_\alpha S^{2p-1}_{l\sin\alpha}$ be the cone of angle $\alpha$ and length $l>0$ over the odd-dimensional sphere $S^{2p-1}$, equipped with the standard metric induced by the im…