Geodesic
Existence of $K$-limits of holomorphic maps
Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 509-514.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $D$ be a complete hyperbolic domain in $\mathbb C^n$, $n>1$, and $N$ a compact Hermitian manifold. We prove a criterion for the existence of the $K$-limit of an arbitrary holomorphic map $f\colon D\to N$ at an arbitrary boundary point $D$ under the condition that $f$ has the corresponding radial limit at this point. 
@article{MZM_2005_77_4_a2,
     author = {P. V. Dovbush},
     title = {Existence of $K$-limits of holomorphic maps},
     journal = {Matemati\v{c}eskie zametki},
     pages = {509--514},
     publisher = {mathdoc},
     volume = {77},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a2/}
}
TY  - JOUR
AU  - P. V. Dovbush
TI  - Existence of $K$-limits of holomorphic maps
JO  - Matematičeskie zametki
PY  - 2005
SP  - 509
EP  - 514
VL  - 77
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a2/
LA  - ru
ID  - MZM_2005_77_4_a2
ER  - 
%0 Journal Article
%A P. V. Dovbush
%T Existence of $K$-limits of holomorphic maps
%J Matematičeskie zametki
%D 2005
%P 509-514
%V 77
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a2/
%G ru
%F MZM_2005_77_4_a2
P. V. Dovbush. Existence of $K$-limits of holomorphic maps. Matematičeskie zametki, Tome 77 (2005) no. 4, pp. 509-514. http://geodesic.mathdoc.fr/item/MZM_2005_77_4_a2/

[1] Royden H. L., “Remarks on the Kobayashi metric”, Lect. Notes in Math., 185, 1971, 125–137 | MR

[2] Kobayashi S., “Invariant distances on complex manifolds and holomorphic mappings”, J. Math. Soc. Japan, 19:4 (1967), 460–480 | MR | Zbl

[3] Kerzman P., Rosay J.-P., “Fonctions plurisubharmoniques d'ehaustion bornées et domaines taut”, Math. Ann., 257:2 (1981), 171–184 | DOI | MR | Zbl

[4] Kirnan P., “On the relations between taut, tight and hyperbolic manifolds”, Bull. Amer. Math. Soc., 76 (1970), 49–51 | DOI | MR

[5] 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

[6] Lehto O., Virtanen K. I., “Boundary behaviour and normal meromorphic functions”, Acta Math., 97 (1957), 47–65 | DOI | MR | Zbl

[7] Fefferman C., “The Bergman kernel and biholomorphic mappings of pseudoconvex domains”, Invent. Math., 26 (1974), 1–65 | DOI | Zbl

[8] Graham I., “Boundary behavior of the Caratheodory and Kobayashi metrics on strongly pseudoconvex domains”, Trans. Amer. Math. Soc., 207 (1975), 219–240 | DOI | MR | Zbl

[9] Dovbush P. V., “O suschestvovanii dopustimykh predelov funktsii mnogikh kompleksnykh peremennykh”, Sib. matem. zh., 28:3 (1987), 373–377

[10] Koranyi A., “Harmonic functions on Hermitian hyperbolic space”, Trans. Amer. Math. Soc., 135 (1969), 507–516 | DOI | Zbl

[11] Chirka E. M., “Teoremy Lindelefa i Fatu v $\mathbb C^n$”, Matem. sb., 92:4 (1973), 622–644