A characterization of domains in $\C^n$ with locally Levi-flat boundaries

Nikolai Nikolov; Pascal J. Thomas

A characterization of domains in $\C^n$ with locally Levi-flat boundaries

Complex Variables 2012-03-16 v2

Authors: Nikolai Nikolov , Pascal J. Thomas

Abstract

A domain in $\C^n$ with Levi-flat boundary near a given point is characterized in terms of the boundary behavior of the Kobayashi or Bergman metrics, or of the Bergman kernel. Some results are given in the case of intermediate values of the rank of the Levi form.

Keywords

Levi-flat boundary Kobayashi metric Bergman metric Bergman kernel several complex variables domain characterization

Cite

@article{arxiv.1111.3024,
  title  = {A characterization of domains in $\C^n$ with locally Levi-flat boundaries},
  author = {Nikolai Nikolov and Pascal J. Thomas},
  journal= {arXiv preprint arXiv:1111.3024},
  year   = {2012}
}

Comments

v2: We have added remarks comparing our results to the previous work of S. Fu, the relevance of which we had not realized

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