Abstract
We define and study m-Stein manifolds which are generalizations of Stein manifolds by using m-subharmonic functions on a non-compact Kähler manifold. We prove that for a non-compact weakly m-complete manifold M, it contains no compact m-local maximum set (\(=\) m-pseudoconcave set) if and only if it is m-Stein.
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22 May 2023
A Correction to this paper has been published: https://doi.org/10.1007/s40879-023-00645-w
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Acknowledgements
The author expresses gratitude to Zbigniew Słodkowski for giving the author a sketch of the proof of Proposition 4.3 and a shorter proof given in the Remark 3.10. The author is also very thankful to him for many stimulating discussions concerning the content of the third and last section. The author sincerely thanks the anonymous referee for improving greatly the presentation of the paper.
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Dedicated to Vyacheslav Pavlovich Zakharyuta on the occasion of his 85th birthday.
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Günyüz, O. A generalization of Stein manifolds. European Journal of Mathematics 8 (Suppl 2), 504–517 (2022). https://doi.org/10.1007/s40879-022-00584-y
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DOI: https://doi.org/10.1007/s40879-022-00584-y