Abstract
In this paper we prove that if \(I\subset M \) is a subset of measure \(0\) in a \(C^2\)-smooth generic submanifold \(M \subset \mathbb C ^n\), then \(M \setminus I\) is non-plurithin at each point of \(M\) in \(\mathbb C ^n\). This result improves a previous result of A. Edigarian and J. Wiegerinck who considered the case where \(I\) is pluripolar set contained in a \(C^1\)-smooth generic submanifold \(M \subset \mathbb C ^n\) (Edigarian and Wiegernick in Math. Z. 266(2):393–398, 2010). The proof of our result is essentially different.
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Acknowledgments
The authors would like to thank Norm Levenberg for his helpful remarks and suggestions on a preliminary version of this paper and for providing them some useful references. This work was supported in part by the agreement between National University of Uzbekistan and Université Paul Sabatier de Toulouse. The authors would like to thank these Universities for their help in organizing meetings of their Mathematical research groups in Tashkent and Toulouse.
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Partially supported by the fundamental research of Khorezm Mamun Academy,Grant -1-024.
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Sadullaev, A., Zeriahi, A. Subsets of full measure in a generic submanifold in \(\mathbb C ^n\) are non-plurithin. Math. Z. 274, 1155–1163 (2013). https://doi.org/10.1007/s00209-012-1110-0
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DOI: https://doi.org/10.1007/s00209-012-1110-0