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Proceedings of the American Mathematical Society
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
Published electronically: January 16, 2009
MathSciNet review: 2480284
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Abstract: Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.


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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: http://dx.doi.org/10.1090/S0002-9939-09-09794-9
PII: S 0002-9939(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.