8 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-Lipschit…

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 $\hat U$…

Degree-at-infinity conjecture. If $X$ and $Y$ are bi-Lipschitz homeomorphic at infinity, then

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…

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…