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.
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The first-named author is supported by a grant from the UGC under DSA-SAP, Phase IV.
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Bharali, G., Stensønes, B. Plurisubharmonic polynomials and bumping. Math. Z. 261, 39–63 (2009). https://doi.org/10.1007/s00209-008-0312-y
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DOI: https://doi.org/10.1007/s00209-008-0312-y