Extension of CR-functions on wedges

Rays condition and extension of CR functions from manifolds of higher type

“…This special case was already treated by the second and third author in [18], giving geometric explanation to a phenomenon discovered by Eastwood-Graham [8,9].…”

“…More recently, Graham and Eastwood [8,9] have observed that only certain Levi form directions lead to the extension. This phenomenon has been further studied by the second and the third author [18], where an invariant geometric way was proposed for selecting those Levi form directions that are responsible for the extension. This has clarified the extension directions arising from the Levi form of M .…”

“…The purpose of this paper is to provide such a description, unifying the results of [1,7,3,10,18] into a single general framework. Roughly speaking, we obtain CR extension of functions on a wedge V ⊂ M in the directions where the leading term of the defining equation of M is positive along certain rays pointing inside V .…”

Extension of CR-functions into weighted wedges through families of nonsmooth analytic discs

“…If all intersections are empty, we say that the complex angle is 0. It is clear that the complex angle is a local biholomorphic invariant of V at p. The angle πα = π/2 plays a special role, as we observed in [ZZ01]. The main reason is that for α > 1/2 and t > 0 small, the power t 1/α dominates the power t 2 that appears in the defining equations of M .…”

“…The main reason is that for α > 1/2 and t > 0 small, the power t 1/α dominates the power t 2 that appears in the defining equations of M . Observe that in the result of [T95] mentioned above, where V is a wedge with generic edge E, the complex angle of V at a point p ∈ E is always π (see [ZZ01]), and hence α > 1/2. In contrast to [T95], the edge E plays a secondary role in Theorem 1.1 and can be seen as a subset of the Lipschitz boundary of V .…”