Model pseudoconvex domains and bumping

Details Model pseudoconvex domains and bumping Model pseudoconvex domains and bumping

2010-10-21

arxiv.org/abs/1010.4451v2

Mathematics

Complex Variables

28 pages; typos corrected; Remarks 2.6 & 2.7 added; clearer proof of Prop. 4.2 given; to appear in IMRN

Scientific paper

The Levi geometry at weakly pseudoconvex boundary points of domains in C^n, n \geq 3, is sufficiently complicated that there are no universal model domains with which to compare a general domain. Good models may be constructed by bumping outward a pseudoconvex, finite-type \Omega \subset C^3 in such a way that: i) pseudoconvexity is preserved, ii) the (locally) larger domain has a simpler defining function, and iii) the lowest possible orders of contact of the bumped domain with \bdy\Omega, at the site of the bumping, are realised. When \Omega \subset C^n, n\geq 3, it is, in general, hard to meet the last two requirements. Such well-controlled bumping is possible when \Omega is h-extendible/semiregular. We examine a family of domains in C^3 that is strictly larger than the family of h-extendible/semiregular domains and construct explicit models for these domains by bumping.

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