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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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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: http://dx.doi.org/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
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.