Geodesic
Inner functions in $C^n$
Matematičeskie zametki, Tome 19 (1976) no. 1, pp. 63-66

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In this paper we prove that if $f$ is a holomorphic function in a strictly pseudoconvex region $D\subset C^n$, $n>1$, with radial limit equal to 1 in modulus at each point of some nonempty open subset $S$ of the boundary of $D$, then $f\equiv\mathrm{const}$ in $D$. 
@article{MZM_1976_19_1_a6,
     author = {A. Sadullaev},
     title = {Inner functions in $C^n$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {63--66},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_1_a6/}
}
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A. Sadullaev. Inner functions in $C^n$. Matematičeskie zametki, Tome 19 (1976) no. 1, pp. 63-66. http://geodesic.mathdoc.fr/item/MZM_1976_19_1_a6/