Regularity of CR mappings of abstract CR structures Academic Article

abstract

• 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).

authors

• Lamel, Bernhard
• Mir, Nordine

published proceedings

• INTERNATIONAL JOURNAL OF MATHEMATICS

author list (cited authors)

• Lamel, B., & Mir, N.

citation count

• 3

complete list of authors

• Lamel, Bernhard||Mir, Nordine

publication date

• January 2020

publisher

• World Scientific Publishing  Publisher

keywords

• Abstract Cr Manifold
• C-infinity Regularity
• Cr Map
• Finite Type
• Formal Subvariety

Digital Object Identifier (DOI)

• 10.1142/S0129167X20500093

start page

• 2050009

end page

• 2050009

volume

• 31

issue

• 1

URL

• http://dx.doi.org/10.1142/s0129167x20500093