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Some generalizations of Chirka's extension theorem

Author: Gautam Bharali
Journal: Proc. Amer. Math. Soc. 129 (2001), 3665-3669
MSC (2000): Primary 32D15
Published electronically: April 26, 2001
MathSciNet review: 1860501
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In this paper, we generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of $S \cup (\partial D \times D)$ - where $D$ is the open unit disc in $\mathbb{C} $ and $S$ is the graph of a continuous $D-$valued function on $\overline{D}$ - to higher dimensions, for certain classes of graphs $S \subseteq \overline{D} \times {D}^{n}, n>1$. In particular, we show that Chirka's extension theorem generalizes to configurations in ${\mathbb{C} }^{n+1}, n>1$, involving graphs of (non-holomorphic) polynomial maps with small coefficients.

References [Enhancements On Off] (What's this?)

  • 1. E.M. Chirka, Generalized Hartogs' lemma and non-linear $\overline{\partial }-$equation, Complex analysis in contemporary mathematics (E.M. Chirka, ed.), Fasis, Moscow (in Russian) (to appear).
  • 2. Evgeni Chirka and Jean-Pierre Rosay, Remarks on the proof of a generalized Hartogs lemma, Ann. Polon. Math. 70 (1998), 43–47. Complex analysis and applications (Warsaw, 1997). MR 1668715
  • 3. Jean Pierre Rosay, A counterexample related to Hartogs’ phenomenon (a question by E. Chirka), Michigan Math. J. 45 (1998), no. 3, 529–535. MR 1653267,

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Additional Information

Gautam Bharali
Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53706

Keywords: Holomorphic extension
Received by editor(s): May 1, 2000
Published electronically: April 26, 2001
Communicated by: Steven R. Bell
Article copyright: © Copyright 2001 American Mathematical Society