Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Lipschitzness of the Lempert and Green functions


Authors: Nikolai Nikolov, Peter Pflug and Pascal J. Thomas
Journal: Proc. Amer. Math. Soc. 137 (2009), 2027-2036
MSC (2000): Primary 32F45, 32U35
DOI: https://doi.org/10.1090/S0002-9939-09-09794-9
Published electronically: January 16, 2009
MathSciNet review: 2480284
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.


References [Enhancements On Off] (What's this?)

  • 1. Z. Blocki, The $ C^{1,1}$ regularity of the pluriscomplex Green function, Michigan Math. J. 47 (2000), 211-215. MR 1793621 (2001k:32057)
  • 2. Z. Blocki, Regularity of the pluriscomplex Green function with several poles, Indiana Univ. Math. J. 50 (2001), 335-351. MR 1857039 (2002g:32043)
  • 3. M. Jarnicki, P. Pflug, Invariant distances and metrics in complex analysis, de Gruyter Exp. Math. 9, de Gruyter, Berlin, New York, 1993. MR 1242120 (94k:32039)
  • 4. M. Jarnicki, P. Pflug, Invariant distances and metrics in complex analysis-revisited, Dissertationes Math. 430 (2005). MR 2167637 (2006h:32010)
  • 5. S. G. Krantz, Regularity of the Kobayashi and Carathéodory metrics on Levi pseudoconvex domains, AIM Preprint Series, Volume 10 (2007).
  • 6. S. G. Krantz, Pseudoconvexity, analytic discs, and invariant metrics, AIM Preprint Series, Volume 10 (2007).
  • 7. N. Nikolov, P. Pflug, Local vs. global hyperconvexity, tautness or $ k$-completeness for unbounded open sets in $ \mathbb{C}^n$, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), IV (2005), 601-618. MR 2207736 (2006j:32002)
  • 8. N. Nikolov, P. Pflug, On the definition of the Kobayashi-Buseman pseudometric, Internat. J. Math. 17 (2006), 1145-1149. MR 2287671 (2007i:32011)
  • 9. N. Nikolov, P. Pflug, On the derivatives of the Lempert functions, Ann. Mat. Pura Appl. (4) 187 (2008), 547-553. MR 2393147
  • 10. W. Zwonek, Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions, Dissertationes Math. 388 (2000). MR 1785672 (2001h:32016)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32F45, 32U35

Retrieve articles in all journals with MSC (2000): 32F45, 32U35


Additional Information

Nikolai Nikolov
Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev 8, 1113 Sofia, Bulgaria
Email: nik@math.bas.bg

Peter Pflug
Affiliation: Carl von Ossietzky Universität Oldenburg, Institut für Mathematik, Postfach 2503, D-26111 Oldenburg, Germany
Email: pflug@mathematik.uni-oldenburg.de

Pascal J. Thomas
Affiliation: Institut de Mathématiques, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 9, France
Email: pthomas@cict.fr

DOI: https://doi.org/10.1090/S0002-9939-09-09794-9
Keywords: Lipschitzness, Lempert function, Kobayashi--Royden pseudometric, pluricomplex Green function, Azukawa pseudometric
Received by editor(s): June 9, 2008
Published electronically: January 16, 2009
Additional Notes: This paper was started during the stay of the first-named author at the Carl von Ossietzky Universität, Oldenburg (October 2007; supported by a grant from the DFG, Az. PF 227/9-1), and was finished during his stay at the Université Paul Sabatier, Toulouse (January 2008).
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society