Talk
Constructing Hölder maps to Carnot groups
Talk by Prof. Dr. Stefan Wenger
Date: 12.12.18 Time: 15.45 - 16.45 Room: ETH HG G 43
Carnot groups equipped with a Carnot metric are subriemannian manifolds. These exhibit interesting (local) geometry that is far from Euclidean. In this talk we mainly focus on the special case of the first Heisenberg group $H$ and study its geometry through Hölder mappings. By a theorem of Züst, which strengthens a result of Gromov and Pansu, every $\alpha$-Hölder map with $\alpha>2/3$ from a Euclidean ball to $H$ factors through some tree. We show that Züst's result is sharp by constructing topologically non-trivial $\alpha$-Hölder maps from the Euclidean $2$-ball and $3$-ball to $H$ for every $\alpha<2/3$. Some of our results generalize to general Carnot groups. Joint work with Robert Young