Model Pseudoconvex Domains and Bumping

Bharali, Gautam (2012) Model Pseudoconvex Domains and Bumping. In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES (21). pp. 4924-4965.

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Abstract

The Levi geometry at weakly pseudoconvex boundary points of domains in C-n, n >= 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 of 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 partial derivative Omega, at the site of the bumping, are realized. When Omega subset of C-n, n >= 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.

Item Type:	Journal Article
Publication:	INTERNATIONAL MATHEMATICS RESEARCH NOTICES
Publisher:	OXFORD UNIV PRESS,
Additional Information:	Copyright for this article belongs to OXFORD UNIV PRESS, ENGLAND
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	11 Dec 2012 06:08
Last Modified:	11 Dec 2012 06:08
URI:	http://eprints.iisc.ac.in/id/eprint/45514

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