Regularity of CR mappings of abstract CR structures

Bernhard Lamel, Nordine Mir

Research output: Contribution to journalArticle


We study the ∞ regularity problem for CR maps from an abstract CR manifold M into some complex Euclidean space N′. We show that if M satisfies a certain condition called the microlocal extension property, then any k-smooth CR map h: M → N′, for some integer k, which is nowhere ∞-smooth on some open subset ω of M, has the following property: for a generic point q of ω, there must exist a formal complex subvariety through h(q), tangent to h(M) to infinite order, and depending in a 1 and CR manner on q. As a consequence, we obtain several ∞ regularity results generalizing earlier ones by Berhanu-Xiao and the authors (in the embedded case).

Original languageEnglish
Article number2050009
JournalInternational Journal of Mathematics
Publication statusAccepted/In press - 1 Jan 2019



  • Abstract CR manifold
  • CR map
  • finite type
  • formal subvariety
  • ∞ regularity

ASJC Scopus subject areas

  • Mathematics(all)

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