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A NOTE ON ZEROS OF BOUNDED HOLOMORPHIC FUNCTIONS IN WEAKLY PSEUDOCONVEX DOMAINS IN ℂ2

  • Ha, Ly Kim (Faculty of Mathematics and Computer Science University of Science Vietnam National University HoChiMinh City (VNU-HCM))
  • Received : 2016.05.17
  • Published : 2017.05.31
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Abstract

Let ${\Omega}$ be a bounded, uniformly totally pseudoconvex domain in ${\mathbb{C}}^2$ with the smooth boundary b${\Omega}$. Assuming that ${\Omega}$ satisfies the negative ${\bar{\partial}}$ property. Let M be a positive, finite area divisor of ${\Omega}$. In this paper, we will prove that: if ${\Omega}$ admits a maximal type F and the ${\check{C}}eck$ cohomology class of the second order vanishes in ${\Omega}$, there is a bounded holomorphic function in ${\Omega}$ such that its zero set is M. The proof is based on the method given by Shaw [27].

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References

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