X-normal mappings
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2003), pp. 71-82.

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This is a survey of achievements in the theory of normal holomorphic mappings. We systematize and present all the results on the subject that are obtained by the author from the beginning of the theory until the date of writing the paper.
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P. V. Dovbush. $X$-normal mappings. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2003), pp. 71-82. https://geodesic-test.mathdoc.fr/item/BASM_2003_3_a6/

[1] Aladro G., “Application of the Kobayashi metric to normal functions of several complex variables”, Util. Math., 37 (1987), 13–24 | MR

[2] Bagemihl F., Seidel W., “Sequential and continuous limits of meromorphic functions”, Ann. Acad. Sci. Fenn., Ser. AI, 280 (1960) | MR | Zbl

[3] Bhenke H., Thullen P., Theorie der Functionen mehrerer komplexer Veränderlichen, 2nd ed., Springer-Verlag, Berlin–Heidelberg, 1970 | MR

[4] Bremermann H. J., “Holomorphic continuation of the kernels and the Bergman metric in several complex variables”, Lectures on Functions of a Complex Variables, Univ. of Michigan Press, Ann Arbor. Mich., 1955, 349–383 | MR

[5] Burns D., Shnider S., Wells R., “On deformations of strongly pseudoconvex domains”, Invent. Math., 46 (1978), 237–253 | DOI | MR | Zbl

[6] Cima J. A., Krantz S. G., “The Lindelöf principle and normal functions of several complex variables”, Duke Math. J., 50 (1983), 303–328 | DOI | MR | Zbl

[7] Math. U. S. S. R. sb., 21:4 (1973), 619–639 | DOI | MR | Zbl

[8] Moscow Univ. Bull., 36 (1981) | MR

[9] Moscow Univ. Bull., 36 (1981) | MR | Zbl

[10] Soviet Math. Dokl., 25 (1982) | MR | Zbl

[11] Math. Notes, 39 (1986), 196–199 | MR | Zbl | Zbl

[12] Siberian Math. J., 28:3 (1987), 411–414 | DOI | MR | Zbl | Zbl

[13] Ucrainian Math. J., 40:6 (1988), 673–676 | DOI | MR | Zbl

[14] Math. Notes, 47:5 (1990), 449–453 | MR | Zbl

[15] Math. Notes, 66:4 (1999), 409–410 | DOI | MR

[16] Dovbush P. V., “The negligible set for normal functions of several complex variables”, Rev. Roumaine de Math. Pures et Appl., 46:1 (2001), 29–35 | MR | Zbl

[17] Dovbush P. V., “Normal functions in convex domains in $\mathbb{C}^n$”, Mathematica Montisnigri, XIV (2001), 79–88 (In Russian) | MR

[18] Soviet Math. Dokl., 26 (1982) | MR | Zbl

[19] Dovbush P. V., Gavrilov V. I., “Normal mappings”, Mathematica Montisnigri, XIV (2001), 5–61 (In Russian) | MR

[20] Funahashi K., “Normal holomorphic mappings and classical theorems of function theory”, Nagoya Math J., 94 (1984), 89–104 | MR | Zbl

[21] Hahn K. T., “Asymptotic behavior of normal mappings of several complex variables”, Canad. J. Math., 36 (1984), 718 | MR | Zbl

[22] Hahn K. T., “Non-tangential limit theorems for normal mappings”, Pacific J. Math., 135:1 (1988), 57–64 | MR | Zbl

[23] Hakim M., Sibony N., “Functions holomorphes bornées et limites tangentielles”, Duke Math. J., 50:1 (1983), 123–141 | DOI | MR

[24] Järvi P., “An extension theorem for normal functions”, Proc. Amer. Math. Soc., 103 (1988), 1171 | DOI | MR | Zbl

[25] Krantz S. G., “Invariant metrics and the boundary behavior of holomorphic functions on domains in $\mathbb{C}^n$”, J. Geom. Anal., 1:2 (1991), 71–97 | MR | Zbl

[26] Lehto O., Virtanen K. I., “Boundary behavior and normal meromorphic functions”, Acta Math., 97 (1957), 47 | DOI | MR | Zbl

[27] Noshiro K., “Contributions to the theory of meromorphic functions in the unit circle”, J. Fac. Sci. Hokaido Imp. Univ., Ser. I, 7 (1938), 149

[28] Ramey W. C., “On the behavior of holomorphic functions near maximum modulus sets”, Math. Ann., 276 (1986), 137–144 | DOI | MR | Zbl

[29] Riihentaus J., “A nulset for normal functions in several variables”, Proc. Amer. Math. Soc., 110 (1990), 923 | DOI | MR | Zbl

[30] Rosay I.-P., “Sur une characterization de la boule parmi les domaines de $\mathbb{C}^n$ par son groupe d'automorphismes”, Ann. Inst. Fourier (Grenoble), 29:1 (1979), 91–97 | MR | Zbl

[31] Rudin W., Function Theory in the Unit Ball in $\mathbb{C}^n$, Springer-Verlag, Berlin, 1983 | Zbl

[32] Stein E. M., Boundary behavior of holomorphic function of several complex variables, Mathematical Notes, Princeton University Press, Princeton, NJ, 1972 | MR | Zbl

[33] Timoney R. M., “Bloch function in several complex variables, 1”, Bull. London Math. Soc., 12:37 (1980), 241–267 | DOI | MR | Zbl

[34] Wong B., “Characterization of the unit ball in $\mathbb{C}^n$ by its automorphism group”, Invent. Math., 41 (1977), 253–257 | DOI | MR | Zbl

[35] Wu H., “Normal families of holomorphic mappings”, Acta Math., 119:3–4 (1967), 193–233 | MR | Zbl

[36] Yosida K., “On a class of meromorphic functions”, Proc. Phys.-Math. Soc. Japan, 3 ser., 16 (1934), 235 | Zbl