6 problems

Let $P\subset H^2$ be an ordinary reduced $n$-gon of minimal width $w$. Let $\widetilde{P}$ denote the regular ordinary reduced $n$-gon of width $w$, and write…

Decagon perimeter conjecture. One has

Strut-side perimeter conjecture. The perimeter $L(P)$ satisfies

Generic polygon image conjecture. The map $\alpha: \mathsf{TS}_{k}\rightarrow\mathsf{TP}_{k+6}$ has image in $\mathsf{TP}^{\mathsf{gen}}_{k+6}$ and is a homeomorphism onto its imag…

Let $\mathcal{J}$ be the functional on the class $\mathcal{P}_n$ of simple polygons used in the paper. A polygon is a critical point of $\mathcal{J}$ when the limit in the paper's…

Let $\mathcal{J}$ be the functional on the class $\mathcal{P}_n$ of simple polygons used in the paper. For $n\in\{3,4\}$, the maximizers of $\mathcal{J}$ over $\mathcal{P}_n$ are r…