5 problems

Let $(\mathbb H,d^{\mathbb H})$ be the Heisenberg group equipped with its Carnot–Carathéodory metric. Lee–Naor conjecture. The metric space $(\mathbb H,d^{\mathbb H})$ does not adm…

Let $A$ be a subset with $\operatorname{diam}(A)\leq D$ of an $n$-dimensional complete Riemannian manifold $(M^n,g)$ with Ricci curvature … Assume that…

Let $D>0$. Let $A$ be a bounded subset with $\operatorname{diam}(A)\leq D$ of an $n$-dimensional complete Alexandrov space $X^n$ with curvature $K\geq -1$. Alexandrov-space embeddi…

Hilbert embeddability conjecture. If $(G,d_S)$ admits a bi-Lipschitz embedding into Hilbert space, then $G$ has an Abelian subgroup of finite index.

Let $n,l\in\mathbb N$, and let the extended space of Grushin type be $\mathbb R^n\times\mathbb R^l$ equipped with the Carnot–Carathéodory distance associated to the horizontal dist…