5 problems

Step-isometry extension conjecture. The map $T$ can be extended to a step-isometry on the whole of $X$.

Isometric transitivity conjecture. If $u\in V$ with $\lVert u\rVert=1$ is a norming order unit, then there exists a surjective linear isometry

Let $d53d$ be a field, let $S_{n,d}(d53d)$ denote the space of homogeneous degree-$d$ polynomials in $n$ variables, and let $\operatorname{d}_{\operatorname{ess}}$ be the essential…

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Let ${\mathcal P}\subset\mathbb R^2$ be a finite point set. An isometry is a distance-preserving map $\varphi:\mathbb R^2\to\mathbb R^2$. The isometry overlap conjecture. There is…