Rad\'o theorem and its generalization for CR-mappings

E. M. Chirka

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arXiv · math/9210201

Rad\'o theorem and its generalization for CR-mappings

E. M. Chirka

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Abstract

The following theorem is proved: Let M be a locally Lipschitz hypersurface in C^n with one-sided extension property at each point (e.g., without analytic discs). Let S be a closed subset of M and f : M \ S ---> C^m \ E is a CR-mapping of class L^{\infty} such that the cluster set of f on S along of Lebesque points of f is contained in a closed complete pluripolar set E. Then there is a CR-mapping \~f : M ---> C^m of class L^{\infty}(M) such that \~f |M\S = f. It follows also that S is removable for CR \cap L^{\infty} (M \ S).

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E. M. Chirka. 1992-11-21. Rad\'o theorem and its generalization for CR-mappings. https://arxiv.org/abs/math/9210201

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