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GEOMETRIC CHARACTERIZATION OF q-PSEUDOCONVEX DOMAINS IN ℂn

  • Khedhiri, Hedi (Departement de Mathematiques Institut prparatoire aux etudes d'inegnieurs de Monastir)
  • Received : 2016.03.01
  • Published : 2017.03.31

Abstract

In this paper, we investigate the notion of q-pseudoconvexity to discuss and describe some geometric characterizations of q-pseudoconvex domains ${\Omega}{\subset}{\mathbb{C}}^n$. In particular, we establish that ${\Omega}$ is q-pseudoconvex, if and only if, for every boundary point, the Levi form of the boundary is semipositive on the intersection of the holomorphic tangent space to the boundary with any (n-q+1)-dimensional subspace $E{\subset}{\mathbb{C}}^n$. Furthermore, we prove that the Kiselman's minimum principal holds true for all q-pseudoconvex domains in ${\mathbb{C}}^p{\times}{\mathbb{C}}^n$ such that each slice is a convex tube in ${\mathbb{C}}^n$.

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