Geometric characterization of q-pseudoconvex domains in Cn
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In this paper, we investigate the notion of $q$-pseudoconvexity to discuss and describe some geometric characterizations of $q$-pseudo\-convex domains $\Omega\subset\C^n$. In particular, we establish that $\Omega$ is $q$-pseudo\-convex, 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 $E\subset\C^n$. Furthermore, we prove that the Kiselman's minimum principal holds true for all $q$-pseudoconvex domains in $\C^p\times\C^n$ such that each slice is a convex tube in $\C^n$.
Abstract
In this paper, we investigate the notion of $q$-pseudoconvexity to discuss and describe some geometric characterizations of $q$-pseudo\-convex domains $\Omega\subset\C^n$. In particular, we establish that $\Omega$ is $q$-pseudo\-convex, 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 $E\subset\C^n$. Furthermore, we prove that the Kiselman's minimum principal holds true for all $q$-pseudoconvex domains in $\C^p\times\C^n$ such that each slice is a convex tube in $\C^n$.
참고문헌 (8)
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