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Geometric and analytic boundary invariants on pseudoconvex domains. Comparison results

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Abstract

We consider for smooth pseudoconvex bounded domains Ω ⊂ ℂn 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 ε1 > 0 for the\(\bar \partial - Neumann\) problem. Furthermore, we consider as local geometric invariants on ∂Ω 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 Ω shows that starting fromn ≥ 3 (essentially) each of these invariants is independent of the remaining ones.

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  1. Universität Wuppertal, Gausstr. 20, 56 Wuppertal 1, Germany

    K. Diederich & G. Herbort

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  1. K. Diederich
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  2. G. Herbort
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Received by John E. Fornaess

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Diederich, K., Herbort, G. Geometric and analytic boundary invariants on pseudoconvex domains. Comparison results. J Geom Anal 3, 237–267 (1993). https://doi.org/10.1007/BF02921392

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