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A characterization of totally real generic submanifolds of strictly pseudoconvex boundaries in $${\mathbb{C}}^ n$$ admitting a local foliation by interpolation submanifolds. (English) Zbl 0716.32013
Let D be a domain in $${\mathbb{C}}^ n$$. A submanifold $$M\subset \partial D$$ is called an interpolation submanifold if for every $$p\in M$$ the tangent space $$T_ p(M)$$ is contained in the maximal complex subspace of $$T_ p(\partial D)$$. The existence of foliations of $$\partial D$$ by interpolation submanifolds is important in characterization of peak and maximum modulus sets on $$\partial D$$. The author proves that each 2- dimensional totally real submanifold of $$\partial D$$ admits local foliations by interpolation submanifolds. Here D is a domain in $${\mathbb{C}}^ 2$$ with $$C^ 1$$ boundary. For $${\mathbb{C}}^ n$$, $$n\geq 3$$, a characterization of totally real sets admitting such foliations is given in terms of the Levi form. Applications to description of maximum modulus sets on $$\partial D$$ for strictly pseudoconvex domais are also given.
Reviewer: A.Russakovskij

##### MSC:
 32V40 Real submanifolds in complex manifolds 32T99 Pseudoconvex domains 32A38 Algebras of holomorphic functions of several complex variables
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##### References:
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