Analytic equivalence of plane curve singularities .
Let , be a domain with -boundary and be a compact set such that is connected. We study univalent analytic extension of CR-functions from to parts of . Call CR-convex if its -convex hull, , satisfies ( denoting the space of functions, which are holomorphic on and continuous up to ). The main theorem of the paper gives analytic extension to , if is CR- convex.
We establish new results on weighted -extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions that we call denominators. We give a collection of examples of these denominators related to the divisor defined by the submanifold.
Let be a bounded, convex and open set with real analytic boundary. Let be the tube with base and let be the Bergman kernel of . If is strongly convex, then is analytic away from the boundary diagonal. In the weakly convex case this is no longer true. In this situation, we relate the off diagonal points where analyticity fails to the Trèves curves. These curves are symplectic invariants which are determined by the CR structure of the boundary of . Note that Trèves curves exist only...