Abstract
We construct explicit supporting manifolds and local holomorphic peak functions as obstructions to the extendability of holomorphic functions on a class of domains not necessarily pseudoconvex in CN, N >2.
Similar content being viewed by others
References
Baouendi, M. S. and Trèves, F. About the holomorphic extension of CR functions,Duke Math. J. 51, 77–107, (1984).
Bedford, E. and Fornæss, J. E. A construction of peak functions on weakly pseudoconvex domains,Ann. of Math. 107, 555–568, (1978).
Bloom, T.C∞-peak functions for pseudoconvex domains of strict type,Duke Math. J. 45, 133–147, (1978).
Fornæss, J. E. Peak points on weakly pseudoconvex domains,Math. Ann. 227, 173–175, (1988).
Fornæss, J. E. and Rea, C. Local holomorphic extendibility and non-extendibility of CR-functions on smooth boundaries,Ann. Scuola Norm. Sup. Pisa 4, 491–502, (1985).
Hakim, M. and Sibony, N. Quelques conditions pour l’existence de fonctions pics dans des domaines pseudoconvex,Duke Math. J. 44, 399–406, (1977).
Kohn, J. J. and Nirenberg, L. A pseudoconvex domain not admitting a holomorphic support function,Math. Ann. 201, 265–268, (1973).
Kolr, M. Convexifiability and supporting functions in ℂ2,Math. Res. Lett. 2, 505–513, (1995).
Rea, C. Prolongement holomorphe des fonctions CR, conditions suffisantes,C. R. Math. Acad. Sci. Paris 297, 163–165, (1983).
Trépreau, J. M. Sur le prolongement holomorphe des fonctions CR définies sur une hypersurface réelle de classeC 2 dans ℂN,Invent. Math. 83, 583–592, (1986).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Siano, A. On the nonextendability of germs of holomorphic functions. J Geom Anal 17, 547–557 (2007). https://doi.org/10.1007/BF02922096
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02922096