Geodesic
The hartogs phenomenon for holomorphically convex K\"ahler manifolds
Izvestiya. Mathematics , Tome 29 (1987) no. 1, pp. 225-232

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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. Bibliography: 10 titles. 
@article{IM2_1987_29_1_a12,
     author = {S. M. Ivashkovich},
     title = {The hartogs phenomenon for holomorphically convex {K\"ahler} manifolds},
     journal = {Izvestiya. Mathematics },
     pages = {225--232},
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1987_29_1_a12/}
}
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S. M. Ivashkovich. The hartogs phenomenon for holomorphically convex K\"ahler manifolds. Izvestiya. Mathematics , Tome 29 (1987) no. 1, pp. 225-232. http://geodesic.mathdoc.fr/item/IM2_1987_29_1_a12/