On the Relationship between D’Angelo \(q\)-Type and Catlin \(q\)-Type

A Correction to this article was published on 13 March 2019

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Abstract

We establish inequalities relating two measurements of the order of contact of \(q\)-dimensional complex varieties with a real hypersurface.

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  • 13 March 2019

    John D���Angelo brought to the authors��� attention the following counterexample to the claim in Corollary 2.11 of [1] that for any ideal I of holomorphic germs the infimum in the definition of the D���Angelo q-type is achieved and equal to the generic value:

  • 13 March 2019

    John D���Angelo brought to the authors��� attention the following counterexample to the claim in Corollary 2.11 of [1] that for any ideal I of holomorphic germs the infimum in the definition of the D���Angelo q-type is achieved and equal to the generic value:

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Acknowledgments

The authors wish to thank Catlin and D’Angelo for a number of essential discussions. Additionally, the authors are very grateful to the referee for his suggestions that greatly improved this paper. The first author was partially supported by a grant of the Ministry of National Education, CNCS-UEFISCDI, project number PN-II-ID-PCE-2012-4-0156. He would like to thank the Department of Mathematics at the University of Pennsylvania for the hospitality during the preparation of part of this article.

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Correspondence to Andreea C. Nicoara.

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Communicated by Steven G. Krantz.

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Brinzanescu, V., Nicoara, A.C. On the Relationship between D’Angelo \(q\)-Type and Catlin \(q\)-Type. J Geom Anal 25, 1701–1719 (2015). https://doi.org/10.1007/s12220-014-9490-5

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Keywords

  • Orders of contact
  • D’Angelo finite \(q\)-type
  • Catlin finite \(q\)-type
  • Finite type domains in \(\mathbb {C}^n\)
  • Pseudoconvexity

Mathematics Subject Classification

  • Primary 32F18
  • 32T25
  • Secondary 32V35
  • 13H15