On Removable Singularities for Cr Functions in Higher Codimension
نویسنده
چکیده
In recent years, several papers (for a complete reference list, see Chirka and Stout [3]) have been published on the subject of removable singularities for the boundary values of holomorphic functions on some domains or hypersurfaces in the complex euclidean space. In this paper, we study the higher codimensional case. Our results for the hypersurface case are weaker than those in [3] and [4], for the smoothness assumption. Note with Tz0M the usual tangent space of a real manifold M ⊂ C n at z0 ∈ M and by T c z0M = Tz0M ∩ JTz0M its complex tangent space, where J denotes the complex structure on TC. M is said to be generic if TzM + JTzM = TzC n for all z ∈ M . We consider continuous distributional solutions of the tangential Cauchy-Riemann equations on M , which will be referred as CR functions on M . Let z0 ∈M . By a wedge of edge M at z0, we mean an open set in C of the form W = {z + η; z ∈ U, η ∈ C},
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