On symmetry of the pluricomplex Green function for ellipsoids

Włodzimierz Zwonek

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 2, page 121-129
  • ISSN: 0066-2216

Abstract

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We show that in the class of complex ellipsoids the symmetry of the pluricomplex Green function is equivalent to convexity of the ellipsoid.

How to cite

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Włodzimierz Zwonek. "On symmetry of the pluricomplex Green function for ellipsoids." Annales Polonici Mathematici 67.2 (1997): 121-129. <http://eudml.org/doc/270751>.

@article{WłodzimierzZwonek1997,
abstract = {We show that in the class of complex ellipsoids the symmetry of the pluricomplex Green function is equivalent to convexity of the ellipsoid.},
author = {Włodzimierz Zwonek},
journal = {Annales Polonici Mathematici},
keywords = {pluricomplex Green function; Lempert function; complex ellipsoid; $k̃_D$-geodesic; plurisubharmonic functions; holomorphic functions; complex ellipsoids},
language = {eng},
number = {2},
pages = {121-129},
title = {On symmetry of the pluricomplex Green function for ellipsoids},
url = {http://eudml.org/doc/270751},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Włodzimierz Zwonek
TI - On symmetry of the pluricomplex Green function for ellipsoids
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 2
SP - 121
EP - 129
AB - We show that in the class of complex ellipsoids the symmetry of the pluricomplex Green function is equivalent to convexity of the ellipsoid.
LA - eng
KW - pluricomplex Green function; Lempert function; complex ellipsoid; $k̃_D$-geodesic; plurisubharmonic functions; holomorphic functions; complex ellipsoids
UR - http://eudml.org/doc/270751
ER -

References

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  1. [Bed-Dem] E. Bedford and J.-P. Demailly, Two counterexamples concerning the pluri-complex Green function in ℂⁿ, Indiana Univ. Math. J. 37 (1988), 865-867. 
  2. [Edi] A. Edigarian, On extremal mappings in complex ellipsoids, Ann. Polon. Math. 62 (1995), 83-96. Zbl0851.32025
  3. [Jar-Pfl] M. Jarnicki and P. Pflug, Invariant Distances and Metrics in Complex Analysis, de Gruyter 1993. 
  4. [Jar-Pfl-Zei] M. Jarnicki, P. Pflug and R. Zeinstra, Geodesics for convex complex ellipsoids, Ann. Scuola Norm. Sup. Pisa 20 (1993), 535-543. Zbl0812.32010
  5. [Kli] M. Klimek, Pluripotential Theory, Oxford University Press, 1991. 
  6. [Lem1] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), 427-474. 
  7. [Pfl-Zwo] P. Pflug and W. Zwonek, The Kobayashi metric for non-convex complex ellipsoids, Complex Variables Theory Appl. 29 (1996), 59-71. Zbl0843.32015
  8. [Pol] E. A. Poletsky, Holomorphic currents, Indiana Univ. Math. J. 42 (1993), 85-144. Zbl0811.32010

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