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 |
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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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