Local vs. global hyperconvexity, tautness or k -completeness for unbounded open sets in 𝒞 n

Nikolai Nikolov[1]; Peter Pflug[2]

  • [1] Institute of Mathematics and Informatics Bulgarian Academy of Sciences 1113 Sofia, Bulgaria
  • [2] Carl von Ossietzky Universität Oldenburg Fachbereich Mathematik Postfach 2503 D-26111 Oldenburg, Germany

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2005)

  • Volume: 4, Issue: 4, page 601-618
  • ISSN: 0391-173X

Abstract

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Some known localization results for hyperconvexity, tautness or k -completeness of bounded domains in ℂ n are extended to unbounded open sets in 𝒞 n .

How to cite

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Nikolov, Nikolai, and Pflug, Peter. "Local vs. global hyperconvexity, tautness or $k$-completeness for unbounded open sets in $\mathcal {C}^n$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 4.4 (2005): 601-618. <http://eudml.org/doc/84573>.

@article{Nikolov2005,
abstract = {Some known localization results for hyperconvexity, tautness or $k$-completeness of bounded domains in $\mathbb \{C\}^n$ are extended to unbounded open sets in $\mathcal \{C\}^n$.},
affiliation = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences 1113 Sofia, Bulgaria; Carl von Ossietzky Universität Oldenburg Fachbereich Mathematik Postfach 2503 D-26111 Oldenburg, Germany},
author = {Nikolov, Nikolai, Pflug, Peter},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {601-618},
publisher = {Scuola Normale Superiore, Pisa},
title = {Local vs. global hyperconvexity, tautness or $k$-completeness for unbounded open sets in $\mathcal \{C\}^n$},
url = {http://eudml.org/doc/84573},
volume = {4},
year = {2005},
}

TY - JOUR
AU - Nikolov, Nikolai
AU - Pflug, Peter
TI - Local vs. global hyperconvexity, tautness or $k$-completeness for unbounded open sets in $\mathcal {C}^n$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2005
PB - Scuola Normale Superiore, Pisa
VL - 4
IS - 4
SP - 601
EP - 618
AB - Some known localization results for hyperconvexity, tautness or $k$-completeness of bounded domains in $\mathbb {C}^n$ are extended to unbounded open sets in $\mathcal {C}^n$.
LA - eng
UR - http://eudml.org/doc/84573
ER -

References

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  1. [1] M. Abate, A characterization of hyperbolic manifolds, Proc. Amer. Math. Soc. 117 (1993), 789–793. Zbl0773.32018MR1128723
  2. [2] Z. Blocki, The complex Monge-Ampère operator in pluripotential theory, Preprint (2004) (http://www.im.uj.edu.pl). Zbl1060.32018
  3. [3] G. T. Buzzard and J. E. Fornaess, An embedding of ℂ in ℂ 2 with hyperbolic complements, Math. Ann. 306 (1996), 539–546. Zbl0864.32013MR1415077
  4. [4] B.-Y. Chen, Bergman completeness of hyperconvex manifolds, Nagoya Math. J. 175 (2004), 165–170. Zbl1061.32010MR2085315
  5. [5] B.-Y. Chen and Z.-H. Zhang, The Bergman metric on a Stein manifold with a bouded plurisubharminc function, Trans. Amer. Math. Soc. 354 (2002), 2997–3009. Zbl0997.32011MR1897387
  6. [6] A. Eastwood, À propos des variétés hyperboliques completes, C. R. Acad. Sci. Paris 280 (1975), 1071–1075. Zbl0301.32021MR414941
  7. [7] F. Forstnerič, Interpolation by holomorphic automorphisms and embeddings in 𝒞 n , J. Geom. Anal. 9 (1999), 93–117. Zbl0963.32006MR1760722
  8. [8] H. Gaussier, Tautness and complete hyperbolicity of domains in ℂ n , Proc. Amer. Math. Soc. 127 (1999), 105–116. Zbl0912.32025MR1458872
  9. [9] N. Kerzman and J.-P. Rosay, Fonctions plurisousharmoniques d’exhaustion bornées et domaines taut, Math. Ann. 257 (1981), 171–184. Zbl0451.32012MR634460
  10. [10] M. Jarnicki and P. Pflug, Remarks on the pluricomplex Green function, Indiana Univ. Math. J. 44 (1995), 535–543. Zbl0848.31007MR1355411
  11. [11] M. Jarnicki and P. Pflug, “Invariant Distances and Metrics in Complex Analysis”, de Gruyter, 1993. Zbl0789.32001MR1242120
  12. [12] M. Jarnicki and P. Pflug, Invariant distances and metrics in complex analysis–revisited, Dissertationes Math. 430 (2005), 1–192. Zbl1085.32005MR2167637
  13. [13] M. Jarnicki, P. Pflug and W. Zwonek, On Bergman completeness of non-hyperconvex domains, Univ. Iagel. Acta Math. 38 (2000), 169–184. Zbl1007.32005MR1812111
  14. [14] S.-H. Park, “Tautness and Kobayashi Hyperbolicty”, Ph. D. thesis, Oldenburg, 2003. Zbl1017.32021
  15. [15] N. Sibony, A class of hyperbolic manifolds, In: “Recent Developments in Several Complex Variables”, J. E. Fornaess (ed.), Ann. Math. Studies 100 (1981), 347–372. Zbl0476.32033MR627768
  16. [16] Do Duc Thai and Pham Viet Duc, On the complete hyperbolicity and the tautness of the Hartogs domains, Internat. J. Math. 11 (2000), 103–111. Zbl1110.32304MR1757893
  17. [17] Do Duc Thai and P. J. Thomas, 𝔻 * -extension property without hyperbolicity, Indiana Univ. Math. J. 47 (1998), 1125-1130. Zbl0927.37024MR1665757
  18. [18] Do Duc Thai and Pham Nguyen Thu Trang, Tautness of locally taut domains in complex spaces, Ann. Polon. Math. 83 (2004), 141–148. Zbl1114.32012MR2111404
  19. [19] V. P. Zaharjuta,Extremal plurisubharmonic functions, Hilbert scales, and the isomorphism of spaces of analytic functions of several variables, Teor. Funkcii, Funkcional. Anal. i Prilozen. 19 (1974), 133–157. MR447632
  20. [20] W. Zwonek, Regularity properties of the Azukawa metric, J. Math. Soc. Japan 52 (2000), 899–914. Zbl0986.32016MR1774635

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