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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

##### MSC:
 32C25 Analytic subsets and submanifolds 32V40 Real submanifolds in complex manifolds
##### Keywords:
regularity of complex tapes; regular submanifold