Subsets of full measure in a generic submanifold in \mathbb C ^n are non-plurithin |
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Authors: | Azimbay Sadullaev Ahmed Zeriahi |
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Institution: | 1. National University of Uzbekistan, 100174, Tashkent, Uzbekistan 2. Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 Route de Narbonne, 31062, Toulouse, France
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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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