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The hull of holomorphy of a nonisotropic ball in a real hypersurface of finite type. (English) Zbl 0734.32007

Let \(M\subset {\mathbb{C}}^ n\) be a smooth hypersurface of finite type and let \(m_ 0\) be the maximum type of points of M. The authors define non- isotropic balls \(B_ M(p,\delta)\) uniformly at all points p of M in terms of the quantities \(\Lambda_ M(p,\delta)=\sum^{m_ 0}_{j=2}\lambda_ j(p)\delta^ j\), where \(\lambda_ j(p)\) involves commutators of length j of vector fields from the complex holomorphic tangent bundle of M which vanish when the Levi form at p vanishes to order (j-2); the balls \(B_ M(p,\delta)\) are ellipsoides centered at p or radius \(\delta\) in the directions of the holomorphic tangent space and of radius \(\Lambda_ M(p,\delta)\) in the totally real direction. The authors show that for f defined on M and satisfying the tangential Cauchy-Riemann equations there, f extends as a holomorphic function to \(B_ M(p,\delta)\). The authors also give maximal-type estimates for their non-isotropic balls and plurisubharmonic functions.

MSC:

32D10 Envelopes of holomorphy
32D15 Continuation of analytic objects in several complex variables
32V99 CR manifolds
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