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Complete hyperbolicity of Hartogs domain

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Abstract.

Let X be a complex space and \({{\varphi: X \rightarrow [-\infty,\infty)}}\) an upper semicontinuous function on X. Consider the Hartogs domain Ωφ(X) given by Ωφ(X)={(z, w)∈X×C: |w| < e −φ(z)}. In this article, some necessary and sufficient conditions on the complete hyperbolicity of Ωφ(X) are established.

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References

  1. Bedford, E., Fornaess, J.: A construction of peak function on weakly pseudoconvex domains. Ann. Math. 107, 555–568 (1978)

    MATH  Google Scholar 

  2. Thai, D.D., Duc, P.V.: On the complete hyperbolicity and the tautness of Hartogs domains. Int. J. Math. 11, 103–111 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Thai, D.D., Thomas, P.J.: D *-extension property without hyperbolicity. Indiana Univ. Math. J. 47, 1125–1130 (1998)

    MATH  Google Scholar 

  4. Fornaess, J., Narasimhan, R.: The Levi problem on complex spaces with singularities. Math. Ann. 248, 47–72 (1980)

    MathSciNet  MATH  Google Scholar 

  5. Gunning, R., Rossi, H.: Analytic Functions of Several Complex Variables. Prentice-Hall Inc. Englewood Cliffs, N.J., 1965

  6. Jarnicki, M., Pflug, P.: Invariant Distances and Metrics in Complex Analysis. Walter de Gruyter Berlin New York, 1993

  7. Kobayashi, S.: Hyperbolic Complex Spaces. Springer Verlag Grundlehren der Mathematischen Wissenschaften 318, (1998)

  8. Krantz, S.: Function Theory of Several Complex Variables. Second edition. Wadsworth and Brooks/Cole Advances Books and Software, 1992

  9. Sibony, N.: Some aspects of weakly pseudoconvex domains. Proceedings of Symposia in Pure Math. 52, 199–231 (1991)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Hanoi University of Education (Dai Hoc Su Pham Hanoi), Cau Giay, TuLiem, Hanoi Vietnam

    Nguyen Quang Dieu & Do Duc Thai

Authors
  1. Nguyen Quang Dieu
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  2. Do Duc Thai
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Correspondence to Nguyen Quang Dieu.

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Mathematics Subject Classification (2000): 32A10, 32C10, 32H20, 32A17

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Dieu, N., Thai, D. Complete hyperbolicity of Hartogs domain. manuscripta math. 112, 171–181 (2003). https://doi.org/10.1007/s00229-003-0388-y

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  • DOI: https://doi.org/10.1007/s00229-003-0388-y

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