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Regularity conditions of complex tapes. (Russian) Zbl 0576.32016
Let M be an oriented \(C^ 1\) real compact submanifold of \({\mathbb{C}}^ n\) of real dimension 2p-1 \((p>1)\). Suppose M is a scarred 2p-1 cycle of class \(C^ 1\). If M is maximally complex, then by the Harvey-Lowson theorem there exists a unique subvariety \(V\subset {\mathbb{C}}^ n\setminus M\) so that \(\partial V=M\). (Then V will be called complex tape.).
The problem of regularity of the set V was previously solved by S. S. Yau [Ann. Math. II. Ser. 113, 67-110 (1981; Zbl 0464.32012)] by using the cohomologies of Kohn-Rossi. In this paper the author gives two theorems on regularity by using another approach.
Reviewer: M.Marinov

32C25 Analytic subsets and submanifolds
32V40 Real submanifolds in complex manifolds
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