10 problems

Let $X\subset\mathbb{C}^n$ and $Y\subset\mathbb{C}^m$ be complex analytic sets with $\dim X=\dim Y=d$. Their germs at zero are bi-Lipschitz homeomorphic if there is a bi-Lipschitz…

Let $LIP(\mathbb{S}^n)$ denote the orientation-preserving homeomorphisms of the $n$-sphere that are bi-Lipschitz. For a bi-Lipschitz map, its isometric distortion is the least…

Metric Zariski multiplicity conjecture. If the germs $(X,0)$ and $(Y,0)$ are ambient bi-Lipschitz homeomorphic, then

Let $G$ be a closed subgroup of the Euclidean group $\operatorname{E}(n)$. A feature map is bi-Lipschitz if it is Lipschitz and preserves orbit-space distances up to multiplicative…

Boundary extra-nice-dimensions conjecture. Any two generic immersions $g$ and $g'$ are bi-Lipschitz $\mathcal{K}_{V}$-equivalent, and the germs $f$ and $f'$ they define are bi-Lips…

Bi-Lipschitz reduction conjecture. For every generalized outward cuspidal domain $U_\psi^n$, there exists a Lipschitz cuspidal function $\hat\psi$, a Lipschitz base domain $\hat U$…

Bi-Lipschitz rigidity conjecture. If 2-attractors are not affinely similar, then they are not bi-Lipschitz equivalent.

Link and double-point image criterion. The map germs $f$ and $g$ are bi-Lipschitz equivalent if and only if $link(f)$ and $link(g)$ are bi-Lipschitz equivalent and the images…

Let $\mathcal{A}=\{\mathsf{R},\mathsf{C},\mathsf{H},\mathsf{O}\}$ be the collection of normed division algebras. For ${\mathsf K}\in\mathcal{A}$ and $n\in\mathsf N$, let…

Let $N$ and $P$ be smooth manifolds of dimensions $n$ and $p$, respectively, and consider the space of proper smooth mappings between them with the Whitney strong topology. Suppose…