H\"{o}lder embeddings into the Heisenberg Group

Friday, September 8, 2023 - 14:00

Thackeray 427

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Yizhou Zeng

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 αH\"{o}lder map f:S1H  admits an αH\"{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.