Extension of CR-functions on wedges

We generalize the extension theorem of Ajrapetyan-Henkin [AH81] and Boggess-Polking [BP82] to wedge-like domains V in a generic manifold M. For each complex tangent vector to M, we introduce its complex angle with respect to V and show that CR-functions on V have natural extension in the direction of the Levi form of any tangent vector whose angle is greater than pi/2. This gives an explanation of the extension phenomenon recently discovered by Eastwood-Graham [EG99,EG01]. We further demonstrate by an example that the angle pi/2 is optimal and cannot be replaced by any smaller angle. We conclude by giving applications to holomorphic extension to a full neighborhood of the reference point.