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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 $\C^n$.
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참고문헌 (8)
참고문헌 신청
A. Sadullaev / 2012 / Potential Theory in the Class of m-Subharmonic Func-tions / Proc. Steklov Inst. Math 279 (1) : 155 ~ 180
C. O. Kiselman / 1978 / The partial Legendre transformation for plurisubharmonic functions / Invent. Math 49 (2) : 137 ~ 148
J. J. Kohn / 1986 / The range of the tangential Cauchy-Riemann operator / Duke Math. J 53 (2) : 525 ~ 545
J. P. Demailly / / Complex Analytic and Differential Geometry
M. Riesz / 1936 / Int´egrale de Riemann-Liouville et potentiels / Acta Sci. Szeged 9 : 1 ~ 42
C. O. Kiselman / 1978 / The partial Legendre transformation for plurisubharmonic functions / Invent. Math 49 (2) : 137 ~ 148
J. J. Kohn / 1986 / The range of the tangential Cauchy-Riemann operator / Duke Math. J 53 (2) : 525 ~ 545
J. P. Demailly / / Complex Analytic and Differential Geometry
M. Riesz / 1936 / Int´egrale de Riemann-Liouville et potentiels / Acta Sci. Szeged 9 : 1 ~ 42
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