Complex geodesics of the minimal ball in n
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 3 (2004) no. 1, p. 53-66
In this note we give a characterization of the complex geodesics of the minimal ball in n . This answers a question posed by Jarnicki and Pflug (cf. [JP], Example 8.3.10)
Classification:  32F45
@article{ASNSP_2004_5_3_1_53_0,
     author = {Pflug, Peter and Youssfi, El Hassan},
     title = {Complex geodesics of the minimal ball in $\mathbb {C}^n$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 3},
     number = {1},
     year = {2004},
     pages = {53-66},
     zbl = {1098.32005},
     mrnumber = {2064967},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2004_5_3_1_53_0}
}
Pflug, Peter; Youssfi, El Hassan. Complex geodesics of the minimal ball in $\mathbb {C}^n$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 3 (2004) no. 1, pp. 53-66. http://www.numdam.org/item/ASNSP_2004_5_3_1_53_0/

[E] A. Edigarian, On extremal mappings in complex ellipsoids, Ann. Polon. Math. 62 (1995), 83-96. | MR 1348220 | Zbl 0851.32025

[G] G. Gentili, Regular complex geodesics in the domain D n ={(z 1 ,...,z n ) n :|z 1 |++|z n |<1}, In: “Complex Analysis III”, C. A. Berenstein (ed.), Lecture Notes in Math. Vol. 1275, Springer-Verlag, Berlin, 1987, pp. 235-252. | MR 922333 | Zbl 0643.32008

[HP] K. T. Hahn - P. Pflug, On a minimal complex norm that extends the real Euclidean norm, Monatsh. Math. 105 (1988), 107-112. | MR 930429 | Zbl 0638.32005

[JP] M. Jarnicki - P. Pflug, “Invariant Distances and Metrics in Complex Analysis”, de Gruyter Expositions in Mathematics, Walter de Gruyter, 1993. | MR 1242120 | Zbl 0789.32001

[K] K. T. Kim, Automorphism group of certain domains with singular boundary, Pacific J. Math. 51 (1991), 54-64. | MR 1127586 | Zbl 0698.32016

[MY] G. Mengotti - E. H. Youssfi, The weighted Bergman projection and related theory on the minimal ball, Bull. Sci. Math. 123 (1999), 501-525. | MR 1713302 | Zbl 0956.32006

[OPY] K. Oeljeklaus - P. Pflug - E. H. Youssfi, The Bergman kernel of the minimal ball and applications, Ann. Inst. Fourier (Grenoble) 47 (1997), 915-928. | Numdam | MR 1465791 | Zbl 0873.32025

[OY] K. Oeljeklaus - E. H. Youssfi, Proper holomorphic mappings and related automorphism groups, J. Geom. Anal. 7 (1997), 623-636. | MR 1669215 | Zbl 0942.32019

[PY] P. Pflug - E. H. Youssfi, The Lu Qi-Keng conjecture fails for strongly convex algebraic domains, Arch. Math. 71 (1998), 240-245. | MR 1637386 | Zbl 0911.32037

[Z] W. Zwonek, Automorphism group of some special domain in n , Univ. Iagel. Acta Math. 33 (1996), 185-189. | MR 1422451 | Zbl 0948.32024