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Some remarks on Hartogs' extension lemma

Authors: Miran Cerne and Manuel Flores
Journal: Proc. Amer. Math. Soc. 138 (2010), 3603-3608
MSC (2010): Primary 32D10; Secondary 32Q60, 32Q65
Published electronically: April 14, 2010
MathSciNet review: 2661559
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Abstract: Motivated by a result and a question by E. M. Chirka we consider the Hartogs' extension property for some connected sets in $ \mathbb{C}\sp 2$ of the form $ K=\Sigma\cup(\partial\Delta\times\overline{\Delta})$, where $ \Sigma$ is a possibly nonconnected compact subset of $ \overline{\Delta}\times\overline{\Delta}\subset\mathbb{C}\sp 2$.

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  • 1. D. E. Barrett and G. Bharali, The role of Fourier modes in extension theorems of Hartogs-Chirka type, Math. Z. 249 (2005), 883-901. MR 2126221 (2005m:32016)
  • 2. G. Bharali, Some generalizations of Chirka's extension theorem, Proc. Amer. Math. Soc. 129 (2001), 3665-3669. MR 1860501 (2002i:32008)
  • 3. M. Černe and M. Flores, Quasilinear $ \bar\partial$-equation on bordered Riemann surfaces, Math. Ann. 335 (2006), 379-403. MR 2221118 (2007b:35247)
  • 4. E. M. Chirka, The generalized Hartogs lemma and the nonlinear $ \overline\partial$-equation, Complex analysis in modern mathematics (Russian), 19-31, FAZIS, Moscow, 2001. MR 1833502 (2002k:32013)
  • 5. E. M. Chirka and J.-P. Rosay, Remarks on the proof of a generalized Hartogs lemma, Complex analysis and applications (Warsaw, 1997). Ann. Polon. Math. 70 (1998), 43-47. MR 1668715 (2000a:32071)
  • 6. E. M. Chirka and E. L. Stout, A Kontinuitätssatz, Topics in complex analysis (Warsaw, 1992), Banach Center Publ., 31, Polish Acad. Sci., Warsaw, 1995, 143-150. MR 1341384 (96g:32026)
  • 7. F. Forstnerič, Stein domains in complex surfaces, J. Geom. Anal. 13 (2003), 77-94. MR 1967038 (2004c:32050)
  • 8. S. Ivashkovich and V. Shevchishin, Structure of the moduli space in a neighborhood of a cusp-curve and meromorphic hulls, Invent. Math. 136 (1999), 571-602. MR 1695206 (2001d:32035)
  • 9. S. Y. Nemirovski, Complex analysis and differential topology on complex surfaces (Russian), Uspekhi Mat. Nauk 54 (1999), 47-74; translation in Russian Math. Surveys 54 (1999), 729-752. MR 1741278 (2000k:32018)
  • 10. R. M. Range, Holomorphic functions and integral representations in several complex variables, Graduate Texts in Mathematics, 108, Springer-Verlag, New York, 1986. MR 847923 (87i:32001)
  • 11. J.-P. Rosay, A counterexample related to Hartogs' phenomenon (a question by E. Chirka), Michigan Math. J. 45 (1998), 529-535. MR 1653267 (2000a:32070)

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Additional Information

Miran Cerne
Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, 1 111 Ljubljana, Slovenia

Manuel Flores
Affiliation: Department of Mathematics, University of La Laguna, 38771 La Laguna, Tenerife, Spain

Keywords: Analytic continuation, Hartogs' extension
Received by editor(s): October 7, 2009
Received by editor(s) in revised form: December 17, 2009, and January 1, 2010
Published electronically: April 14, 2010
Additional Notes: The first author was supported in part by grant Analiza in geometrija P1-0291 from the Ministry of Higher Education, Science and Technology of the Republic of Slovenia.
The second author was supported in part by a grant from Ministerio de Ciencia y Tecnología, MTM 2007/65009.
Dedicated: Dedicated to Professor J. M. Méndez on the occasion of his 60th birthday
Communicated by: Franc Forstneric
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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