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Some remarks on Hartogs' extension lemma
Author(s):
Miran
Cerne;
Manuel
Flores
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3603-3608.
MSC (2010):
Primary 32D10;
Secondary 32Q60, 32Q65
Posted:
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  of the form  , where  is a possibly nonconnected compact subset of  .
References:
-
- 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
 -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
 -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
Email:
miran.cerne@fmf.uni-lj.si
Manuel
Flores
Affiliation:
Department of Mathematics, University of La Laguna, 38771 La Laguna, Tenerife, Spain
Email:
mflores@ull.es
DOI:
10.1090/S0002-9939-10-10367-0
PII:
S 0002-9939(10)10367-0
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
Posted:
April 14, 2010
Additional Notes:
The first author was supported in part by grant {\it 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
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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