Lipschitzness of the Lempert and Green functions
HTML articles powered by AMS MathViewer
- by Nikolai Nikolov, Peter Pflug and Pascal J. Thomas PDF
- Proc. Amer. Math. Soc. 137 (2009), 2027-2036 Request permission
Abstract:
Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.References
- Zbigniew Błocki, The $C^{1,1}$ regularity of the pluricomplex Green function, Michigan Math. J. 47 (2000), no. 2, 211–215. MR 1793621, DOI 10.1307/mmj/1030132530
- Zbigniew Błocki, Regularity of the pluricomplex Green function with several poles, Indiana Univ. Math. J. 50 (2001), no. 1, 335–351. MR 1857039, DOI 10.1512/iumj.2001.50.2035
- Marek Jarnicki and Peter Pflug, Invariant distances and metrics in complex analysis, De Gruyter Expositions in Mathematics, vol. 9, Walter de Gruyter & Co., Berlin, 1993. MR 1242120, DOI 10.1515/9783110870312
- Marek Jarnicki and Peter Pflug, Invariant distances and metrics in complex analysis—revisited, Dissertationes Math. 430 (2005), 192. MR 2167637, DOI 10.4064/dm430-0-1
- S. G. Krantz, Regularity of the Kobayashi and Carathéodory metrics on Levi pseudoconvex domains, AIM Preprint Series, Volume 10 (2007).
- S. G. Krantz, Pseudoconvexity, analytic discs, and invariant metrics, AIM Preprint Series, Volume 10 (2007).
- Nikolai Nikolov and Peter Pflug, Local vs. global hyperconvexity, tautness or $k$-completeness for unbounded open sets in $\Bbb C^n$, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4 (2005), no. 4, 601–618. MR 2207736
- Nikolai Nikolov and Peter Pflug, On the definition of the Kobayashi-Buseman pseudometric, Internat. J. Math. 17 (2006), no. 10, 1145–1149. MR 2287671, DOI 10.1142/S0129167X06003874
- Nikolai Nikolov and Peter Pflug, On the derivatives of the Lempert functions, Ann. Mat. Pura Appl. (4) 187 (2008), no. 3, 547–553. MR 2393147, DOI 10.1007/s10231-007-0056-z
- Włodzimierz Zwonek, Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions, Dissertationes Math. (Rozprawy Mat.) 388 (2000), 103. MR 1785672, DOI 10.4064/dm388-0-1
Additional Information
- Nikolai Nikolov
- Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev 8, 1113 Sofia, Bulgaria
- MR Author ID: 332842
- Email: nik@math.bas.bg
- Peter Pflug
- Affiliation: Carl von Ossietzky Universität Oldenburg, Institut für Mathematik, Postfach 2503, D-26111 Oldenburg, Germany
- MR Author ID: 139035
- 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
- MR Author ID: 238303
- Email: pthomas@cict.fr
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2480284