The Michigan Mathematical Journal

A generalization to the q-convex case of a theorem of Fornæss and Narasimhan

Anca Popa-Fischer

Full-text: Open access

Article information

Source
Michigan Math. J., Volume 50, Issue 3 (2002), 483-492.

Dates
First available in Project Euclid: 4 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1039029978

Digital Object Identifier
doi:10.1307/mmj/1039029978

Mathematical Reviews number (MathSciNet)
MR1852300

Zentralblatt MATH identifier
1026.32061

Citation

Popa-Fischer, Anca. A generalization to the q -convex case of a theorem of Fornæss and Narasimhan. Michigan Math. J. 50 (2002), no. 3, 483--492. doi:10.1307/mmj/1039029978. https://projecteuclid.org/euclid.mmj/1039029978


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References

  • A. Andreotti and H. Grauert, Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France 90 (1962), 193--259.
  • L. Bungart, Piecewise smooth approximations to $q$-plurisubharmonic functions, Pacific J. Math. 142 (1990), 227--244.
  • M. Colţoiu, A note on Levi's problem with discontinuous functions, Enseign. Math. (2) 31 (1985), 299--304.
  • ------, $n$-Concavity of $n$-dimensional complex spaces, Math. Z. 210 (1992), 203--206.
  • J. P. Demailly, Cohomology of $q$-convex spaces in top degrees, Math. Z. 204 (1990), 283--295.
  • K. Diederich and J. E. Fornæss, Smoothing $q$-convex functions and vanishing theorems, Invent. Math. 82 (1985), 291--305.
  • ------, Smoothing $q$-convex functions in the singular case, Math. Ann. 273 (1986), 665--671.
  • J. E. Fornæss and R. Narasimhan, The Levi problem on complex spaces with singularities, Math. Ann. 248 (1980), 47--72.
  • O. Fujita, Domaines pseudoconvexes d'ordre général et fonctions pseudoconvexes d'ordre général, J. Math. Kyoto Univ. 30 (1990), 637--649.
  • L. R. Hunt and J. J. Murray, $q$-Plurisubharmonic functions and a generalized Dirichlet problem, Michigan Math. J. 25 (1978), 299--316.
  • K. Matsumoto, Boundary distance functions and $q$-convexity of pseudoconvex domains of general order in Kähler manifolds, J. Math. Soc. Japan 48 (1996), 85--107.
  • M. Peternell, Continuous $q$-convex exhaustion functions, Invent. Math. 85 (1986), 249--262.
  • A. Popa, Sur un théorème de Fornæss et Narasimhan, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999), 11--14.
  • A. Popa-Fischer, Generalized Kähler metrics on complex spaces and a supplement to a theorem of Fornæss and Narasimhan, Ph.D. dissertation, Bergische Universität Wuppertal, 2000.
  • R. Richberg, Stetige streng pseudokonvexe Funktionen, Math. Ann. 175 (1968), 257--286.
  • Y.-T. Siu, Every Stein subvariety admits a Stein neighborhood, Invent. Math. 38 (1976/77), 89--100.
  • Z. Slodkowski, The Bremmermann--Dirichlet problem for $q$-plurisubharmonic functions, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 11 (1984), 303--326.