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

Nikolai Nikolov (1) , Pascal J. Thomas (2)

1 Institute of Mathematics and Informatics
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Levi form; Bergman pseudometric; Kobayashi-Royden pseudometric; multitype

Domaines: Variables complexes [math.CV]

Nikolai Nikolov, Pascal J. Thomas. A characterization of domains in $C^n$ with locally Levi-flat boundaries. 2011. ⟨hal-00641735⟩