A variant of Gromov's problem on Hölder equivalence of Carnot groups

Derek Jung

It is unknown if there exists a locally $\alpha$-Hölder homeomorphism $f:{\mathbb{R}}^3\to {\mathbb{H}}^1$ for any $\frac{1}{2}<\alpha \le \frac{2}{3}$, although the identity map $\mathbb{R}^3\t…