Regularity of CR maps into uniformly pseudoconvex hypersurfaces

14.01.2021 09:00 - 10:30

Josef Greilhuber (University of Vienna)

Given CR submanifolds $M\in \mathbb{C}^N$ and $M' \in \mathbb{C}^{N'}$, the existence of highly irregular CR maps $h:M \rightarrow M'$ is closely related to existence of complex curves contained in the target manifold $M'$.

Here we will be interested in pseudoconvex hypersurfaces $M'$ whose Levi form is of constant rank, as these are foliated by complex manifolds and thus provide ample opportunity for irregular maps to arise. Introducing an invariant $\nu$ measuring the $2$-degeneracy of $M'$, we will arrive at rather sharp regularity results depending only on $\nu$ and the CR dimension of $M$.

Bernhard Lamel