Friday, September 8, 2023 - 14:00
Thackeray 427
Abstract or Additional Information
The Heisenberg group, Hn, is a sub-Riemannian manifold equipped with the Carnot-Caratheodory metric dc. It is homeomorphic to R2n+1 but it has Hausdorff dimension of 2n+2. In this talk, we will discuss some recent progress about H\"{o}lder embeddings into Hn. In particular, Wenger and Young developed a variant of Dehn function, then proved that for any α∈(0,2/3), an α−H\"{o}lder map f:S1→H admits an α−H\"{o}lder extension to D2. Moreover, we will introduce a theorem about non-existence of H\"{o}lder embeddings by Haj\l{}asz and Schikorra, which generalizes a result of Gromov.