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Geometric and analytic boundary invariants on pseudoconvex domains. Comparison results. (English) Zbl 0786.32016
The authors’ abstract: “We consider for smooth pseudoconvex bounded domains \(\Omega \subset \mathbb{C}^ n\) of finite type as local analytic invariants on the boundary the growth orders of the Bergman kernel and the Bergman metric and the best possible order of subellipticity \(\varepsilon_ 1>0\) for the \(\overline\partial\)-Neumann problem. Furthermore, we consider as local geometric invariants on \(\partial\Omega\) the order of extendability, the exponent of extendability, the 1-type, and the multitype. Various new inequalities between these invariants are proved, giving in particular analytic information from geometric input. On the other hand, a careful consideration of several series of examples of such domains \(\Omega\) shows that starting from \(n \geq 3\) (essentially) each of these invariants is independent of the remaining ones”.

MSC:
32T99 Pseudoconvex domains
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32F45 Invariant metrics and pseudodistances in several complex variables
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
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