Complex geodesics of the minimal ball in ℂ n

Peter Pflug[1]; El Hassan Youssfi[2]

  • [1] Institut für Mathematik Postfach 2503 Universität Oldenburg 26111 Oldenburg, Germany
  • [2] LATP, U.M.R. C.N.R.S. 6632 CMI, Université de Provence 39 Rue F-Joliot-Curie 13453 Marseille Cedex 13, France

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2004)

  • Volume: 3, Issue: 1, page 53-66
  • ISSN: 0391-173X

Abstract

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In this note we give a characterization of the complex geodesics of the minimal ball in ℂ n . This answers a question posed by Jarnicki and Pflug (cf. [JP], Example 8.3.10)

How to cite

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Pflug, Peter, and Youssfi, El Hassan. "Complex geodesics of the minimal ball in $\mathbb {C}^n$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 3.1 (2004): 53-66. <http://eudml.org/doc/84528>.

@article{Pflug2004,
abstract = {In this note we give a characterization of the complex geodesics of the minimal ball in $\mathbb \{C\}^\{n\}$. This answers a question posed by Jarnicki and Pflug (cf. [JP], Example 8.3.10)},
affiliation = {Institut für Mathematik Postfach 2503 Universität Oldenburg 26111 Oldenburg, Germany; LATP, U.M.R. C.N.R.S. 6632 CMI, Université de Provence 39 Rue F-Joliot-Curie 13453 Marseille Cedex 13, France},
author = {Pflug, Peter, Youssfi, El Hassan},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {53-66},
publisher = {Scuola Normale Superiore, Pisa},
title = {Complex geodesics of the minimal ball in $\mathbb \{C\}^n$},
url = {http://eudml.org/doc/84528},
volume = {3},
year = {2004},
}

TY - JOUR
AU - Pflug, Peter
AU - Youssfi, El Hassan
TI - Complex geodesics of the minimal ball in $\mathbb {C}^n$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2004
PB - Scuola Normale Superiore, Pisa
VL - 3
IS - 1
SP - 53
EP - 66
AB - In this note we give a characterization of the complex geodesics of the minimal ball in $\mathbb {C}^{n}$. This answers a question posed by Jarnicki and Pflug (cf. [JP], Example 8.3.10)
LA - eng
UR - http://eudml.org/doc/84528
ER -

References

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  1. [E] A. Edigarian, On extremal mappings in complex ellipsoids, Ann. Polon. Math. 62 (1995), 83-96. Zbl0851.32025MR1348220
  2. [G] G. Gentili, Regular complex geodesics in the domain D n = { ( z 1 , ... , z n ) ∈ ℂ n : | z 1 | + ⋯ + | z n | l t ; 1 } , In: “Complex Analysis III”, C. A. Berenstein (ed.), Lecture Notes in Math. Vol. 1275, Springer-Verlag, Berlin, 1987, pp. 235-252. Zbl0643.32008MR922333
  3. [HP] K. T. Hahn – P. Pflug, On a minimal complex norm that extends the real Euclidean norm, Monatsh. Math. 105 (1988), 107-112. Zbl0638.32005MR930429
  4. [JP] M. Jarnicki – P. Pflug, “Invariant Distances and Metrics in Complex Analysis”, de Gruyter Expositions in Mathematics, Walter de Gruyter, 1993. Zbl0789.32001MR1242120
  5. [K] K. T. Kim, Automorphism group of certain domains with singular boundary, Pacific J. Math. 51 (1991), 54-64. Zbl0698.32016MR1127586
  6. [MY] G. Mengotti – E. H. Youssfi, The weighted Bergman projection and related theory on the minimal ball, Bull. Sci. Math. 123 (1999), 501-525. Zbl0956.32006MR1713302
  7. [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. Zbl0873.32025MR1465791
  8. [OY] K. Oeljeklaus – E. H. Youssfi, Proper holomorphic mappings and related automorphism groups, J. Geom. Anal. 7 (1997), 623-636. Zbl0942.32019MR1669215
  9. [PY] P. Pflug – E. H. Youssfi, The Lu Qi-Keng conjecture fails for strongly convex algebraic domains, Arch. Math. 71 (1998), 240-245. Zbl0911.32037MR1637386
  10. [Z] W. Zwonek, Automorphism group of some special domain in ℂ n , Univ. Iagel. Acta Math. 33 (1996), 185-189. Zbl0948.32024MR1422451

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