3 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…