Regularity of CR mappings of abstract CR structures Academic Article uri icon


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

published proceedings


author list (cited authors)

  • Lamel, B., & Mir, N.

citation count

  • 3

complete list of authors

  • Lamel, Bernhard||Mir, Nordine

publication date

  • January 2020