Geodesic
Two-dimensional spheres in the boundaries of strictly pseudoconvex domains in $\mathbf C^2$
Izvestiya. Mathematics , Tome 39 (1992) no. 3, pp. 1151-1187

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It is shown that there exists a Levi-flat surface in $\mathbf C^2$ with boundary on a given two-dimensional sphere that lies in the boundary of a strictly pseudoconvex domain and is totally real everywhere except at a finite number of elliptic and hyperbolic points. 
@article{IM2_1992_39_3_a3,
     author = {N. G. Kruzhilin},
     title = {Two-dimensional spheres in the boundaries of strictly pseudoconvex domains in $\mathbf C^2$},
     journal = {Izvestiya. Mathematics },
     pages = {1151--1187},
     publisher = {mathdoc},
     volume = {39},
     number = {3},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_39_3_a3/}
}
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N. G. Kruzhilin. Two-dimensional spheres in the boundaries of strictly pseudoconvex domains in $\mathbf C^2$. Izvestiya. Mathematics , Tome 39 (1992) no. 3, pp. 1151-1187. http://geodesic.mathdoc.fr/item/IM2_1992_39_3_a3/