3 problems

Let $X$ and $Y$ be metric-measure spaces, and let a Measured Simplexwise Distribution be the metric-measure invariant obtained from simplexwise distance data at a parameter $h$. Me…

Let $C\subset\mathbb R^n$ be a cloud and let $\mathrm{SDD}(C;h)$ denote its Simplexwise Distance Distribution at scale $h$, for some integer $h\leq n$. Simplexwise Distance Distrib…

Curve Histogram Conjecture. The distance histogram $H_{\mathcal{X}}$ determines a fully regular plane curve up to isometry.