Generalized models and local invariants of Kohn-Nirenberg domains
| Authors | |
|---|---|
| Year of publication | 2008 |
| Type | Article in Periodical |
| Magazine / Source | Matematische Zeitschrift |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Kohn-Nirenberg phenomenon; convexifiability; generalized models; pseudoconvexity; finite type |
| Description | 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. This paper gives 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 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. |
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