Plurisubharmonic polynomials and bumping |
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Authors: | Gautam Bharali Berit Stensønes |
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Institution: | (1) Department of Mathematics, Indian Institute of Science, C.V. Raman Avenue, Bangalore, 560012, India;(2) Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA |
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Abstract: | We wish to study the problem of bumping outwards a pseudoconvex, finite-type domain 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 , 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 . 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.
The first-named author is supported by a grant from the UGC under DSA-SAP, Phase IV. |
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Keywords: | Bumping Finite-type domain Plurisubharmonic function Weighted-homogeneous function |
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