4 problems

Join projection conjecture. The map $\pi_W$ is a homeomorphism, without excepting a set of measure zero.

A Fenn graph is the graph $G(f)$ of a continuous map $f:\mathbb{R}^{2}\to\mathbb{R}$ over a compact convex domain $D\subset\mathbb{R}^{2}$ satisfying Fenn's boundary conditions. Le…

A saddle surface is the graph $G(f)$ of a continuous map $f:\mathbb{R}^{2}\to\mathbb{R}$ satisfying the saddle-surface conditions, with center at the origin. Let…

Square-like quadrilateral conjecture. There is a square-like quadrilateral inscribed in any embedding of $S^1$ in $\mathbb{R}^n$.