Normal forms and degenerate CR singularities
نویسندگان
چکیده
منابع مشابه
Polynomial Approximation, Local Polynomial Convexity, and Degenerate Cr Singularities
We begin with the following question: given a closed disc D ⋐ C and a complex-valued function F ∈ C(D), is the uniform algebra on D generated by z and F equal to C(D) ? When F ∈ C 1 (D), this question is complicated by the presence of points in the surface S := graph D (F) that have complex tangents. Such points are called CR singularities. Let p ∈ S be a CR singularity at which the order of co...
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We begin with the following question: given a closed disc D b C and a complexvalued function F ∈ C(D), is the uniform algebra on D generated by z and F equal to C(D) ? When F ∈ C1(D), this question is complicated by the presence of points in the surface S := graphD(F ) that have complex tangents. Such points are called CR singularities. Let p ∈ S be a CR singularity at which the order of contac...
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A compact subset K ⊂ C is said to be polynomially convex if for every point ζ / ∈ K, there exists a holomorphic polynomial P such that P (ζ) = 1 and supK |P | < 1. K is said to be locally polynomially convex at a point p ∈ K if there exists a closed ball B(p) centered at p such that K ∩ B(p) is polynomially convex. In general, it is difficult to determine whether a given compact K ⊂ C is polyno...
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We propose two constructions extending the Chern-Moser normal form to non-integrable Levi-nondegenerate (hypersurface type) almost CR structures. One of them translates the ChernMoser normalization into pure intrinsic setting, whereas the other directly extends the (extrinsic) Chern-Moser normal form by allowing non-CR embeddings that are in some sense “maximally CR”. One of the main difference...
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ژورنال
عنوان ژورنال: Complex Variables and Elliptic Equations
سال: 2016
ISSN: 1747-6933,1747-6941
DOI: 10.1080/17476933.2016.1170819