The Journal of Geometric Analysis

, Volume 9, Issue 3, pp 429–456 | Cite as

Removable singularities ofL p CR-functions on hypersurfaces



Let H be a C2 hypersurface in ℂn, n ≥ 3, and let M be a generic submanifold of H of real codimension one. We describe classes of compact removable singularities K for Lp-solutions of the tangential Cauchy-Riemann equations on H under the conditions K ⊂ M, 1 ≤ p ≤ ∞. Removability is understood here in the classical sense, but new effects occur based on compulsory analytic extension and envelopes of holomorphy. The classical theory gives results only in the case p > 1. But even for p > 1, removable singularities for Lp-solutions of the tangential Cauchy-Riemann equations may be metrically much more massive than the classical theory predicts. The results for p = 1 are close to corresponding results on removability in the sense of analytic extension justifying the name “removability” for the latter subject. No Levi-form condition on H is posed and the description is given intrinsically in terms of the CR-structure of M. This may be interesting in connection with generalizations, for example, to more general CR-manifolds instead of H.

Math Subject Classifications

32A35 32D15 32D20 32A40 32C16 32D10 32F40 

Key Words and Phrases

tangential Cauchy-Riemann operators CR-manifolds CR-orbits minimal CR-invariant sets removable singularities for CR-functions of classLlocp 


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Copyright information

© Mathematica Josephina, Inc. 1999

Authors and Affiliations

  1. 1.Mathematical DepartmentUppsala UniversityUppsalaSweden

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