Plurisubharmonic polynomials and bumping

Bharali, Gautam and Stensones, Berit (2009) Plurisubharmonic polynomials and bumping. In: Mathematische Zeitschrift, 261 (1). pp. 39-63.

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Abstract

We wish to study the problem of bumping outwards a pseudoconvex, finite-type domain $${\Omega \subset \mathbb{C}^{n}}$$ in such a way that pseudoconvexity is preserved and such that the lowest possible orders of contact of the bumped domain with ∂Ω, at the site of the bumping, are explicitly realised. Generally, when $${\Omega \subset \mathbb{C}^{n}, n \geq 3}$$ , the known methods lead to bumpings with high orders of contact—which are not explicitly known either—at the site of the bumping. Precise orders are known for h-extendible/semiregular domains. This paper is motivated by certain families of non-semiregular domains in $${\mathbb{C}^3}$$ . These families are identified by the behaviour of the least-weight plurisubharmonic polynomial in the Catlin normal form. Accordingly, we study how to perturb certain homogeneous plurisubharmonic polynomials without destroying plurisubharmonicity.

Item Type:	Journal Article
Publication:	Mathematische Zeitschrift
Publisher:	Springer
Additional Information:	Copyright of this article belongs to Springer.
Keywords:	Bumping;Finite-type domain;Plurisubharmonic function; Weighted-homogeneous function.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	26 Sep 2009 08:42
Last Modified:	19 Sep 2010 04:57
URI:	http://eprints.iisc.ac.in/id/eprint/17530

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