Mathematische Zeitschrift

, Volume 261, Issue 1, pp 39–63 | Cite as

Plurisubharmonic polynomials and bumping

  • Gautam BharaliEmail author
  • Berit Stensønes


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.


Bumping Finite-type domain Plurisubharmonic function Weighted-homogeneous function 

Mathematics Subject Classification (2000)

Primary 32F05 32T25 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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