Generalized models and local invariants of Kohn-Nirenberg domains. (English) Zbl 1137.32014

Summary: The main obstruction for constructing holomorphic reproducing kernels of Cauchy type on weakly pseudoconvex domains is the Kohn-Nirenberg phenomenon, i.e., nonexistence of supporting functions and local nonconvexifiability. In this paper we give an explicit verifiable characterization of weakly pseudoconvex but locally nonconvexifiable hypersurfaces of finite type in dimension two. It is expressed in terms of a generalized model, which captures the local geometry of the hypersurface both in the complex tangential and nontangential directions. As an application we obtain a new class of nonconvexifiable pseudoconvex hypersurfaces with convex models.


32T25 Finite-type domains
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