Abstract
This is a report on some joint work with Professor J.A. Cima concerning removable singularities theorems. The general situation is as follows: We are given a bounded domain Ω in ℂn, a complex-analytic subvariety V of Ω, and a holomorphic function f on Ω - V. We seek to determine conditions on f and possibly on V such that f extends holomorphically to Ω and the extended function belongs to a specified class of functions.
Partially supported by the National Sciences and Engineering Research Council of Canada.
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Bibliography
J.M. Anderson, J. Clunie, and C. Ponunerenke, “On Bloch functions and normal functions,” J. Reine Amgew. Math., 270 (1974), 12–37.
U. Cegrell, “Removable singularity sets for analytic functions having modulus with bounded Laplace mass,” Prepring, Mill University and Uppsala Universitet.
J.A. Cima and I.R. Graham, “On the extension of holomorphic functions with growth conditions across analytic subvarieties,” Mich. Math. J. 28 (1981), 241–256.
J.A. Cima and I.R. Graham, “Removable singularities for Bloch and BMO functions,” Preprint, University of North Carolina at Chapel Hill and University of Toronto.
I.R. Graham, “Zero sets and extension theorems for the Hp and Nevanlinna classes on the unit ball and polydisc in <!-Math-!>,” to appear in the Proceedings of the Beijing Symposium on Differential Geometry and Partial Differential Equations, Science Press, China and Van Nostrand Reinhold.
K.T. Hahn, “Holomorphic mappings of the hyperbolic space into the complex Euclidean space and the Bloch theorem,” Can. J. Math. 27 (1975), 446–458.
K.T. Hahn, “Quantitative Bloch’s theorem for certain classes of holomorphic mappings of the ball into Pnℂ,” J. Reine Angew. Math. 283 (1976), 99–109.
C. Pommerenke, “Schlichte Funktionen und analytische Funktionen von beschränkler mittlerer Oszillation,” Comment. Math. Helv. 52 (1977), 591–602.
R.M. Timoney, “Bloch functions in several complex variables, I,” Bull. London Math. Soc. 12 (1980), 241–267.
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© 1984 Birkhäuser Boston, Inc.
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Graham, I.R. (1984). Removable Singularities for Holomorphic Functions which Satisfy the Area-BMO Condition. In: Kohn, J.J., Remmert, R., Lu, QK., Siu, YT. (eds) Several Complex Variables. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5296-2_19
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DOI: https://doi.org/10.1007/978-1-4612-5296-2_19
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