Abstract:
It is said that the Hartogs phenomenon occurs for a complex manifold $Y$ if every holomorphic mapping $f$ of a domain $D$ over $\mathbf C^n$ into $Y$ extends to a holomorphic mapping $\widetilde f$ of the envelope of holomorphy $\widetilde D$ into $Y$. In this paper it is proved that a holomorphically convex Kähler manifold $Y$ exhibits the Hartogs phenomenon if and only if $Y$ contains no rational curves.
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