4 problems

Let $d\ge 2$ and let $P$ be an edge-scribable $(d+1)$-polytope. A polytope is Möbius unique if its edge-scribed realizations are equivalent under Möbius transformations. Möbius uni…

Let $Q(k,\theta)$ denote the quotient studied in the paper, with $0<k<1$ and $0<\theta<2\pi$. The sharp quotient bounds conjecture. For all such $k$ and $\theta$, … and … The conje…

The sector cross-ratio supremum conjecture. One has

Let $n$ and $r$ be the dimensions under consideration, and let $f:\hat{\mathbb{R}}^n\to\hat{\mathbb{R}}^n$ be a map that sends every $r$-dimensional sphere into an $r$-dimensional…