Deformations of irregular maps from smooth into analytic CR submanifolds

12.11.2020 09:00 - 10:30

Josef Greilhuber (University of Vienna)

Due to a theorem by Nordine Mir, any sufficiently regular, but nowhere smooth CR map from a minimal, real analytic CR submanifold into another real analytic submanifold may locally be deformed to a smooth map. If both source and target manifold are just smooth, the deformation, although formally still constructable (due to Lamel and Mir), might diverge.
However, several phenomena hint at the possibility that for the existence of a convergent deformation, only the analyticity of the target manifold is crucial. This is the case e.g. if the target manifold does not contain any complex varieties of dimension greater than one.

Bernhard Lamel