A two-sided H. Lewy extension phenomenon

Authors:
L. R. Hunt and M. Kazlow

Journal:
Proc. Amer. Math. Soc. **74** (1979), 95-100

MSC:
Primary 32D10

MathSciNet review:
521879

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Abstract: Let *M* be a real -dimensional CR-manifold in . We are interested in finding conditions on *M* near a point which imply that all CR-function on *M* extend to holomorphic functions in some fixed neighborhood of *p* in . Of course if *M* is a real hypersurface, it is known that *M* having eigenvalues of opposite sign in its Levi form at *p* will give us such an extension result. If we view the Levi form at a point on a general CR-manifold *M* as a quadratic map from the holomorphic tangent space to the normal space of the real tangent space in , and if this map is surjective, then we prove our CR-functions extend to holomorphic functions in an open neighborhood of the point. We also show that if the real codimension of *M* in is 2, and if the Levi form is totally indefinite, then the Levi form is onto as a quadratic map, and hence we have our extension theory.

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DOI:
https://doi.org/10.1090/S0002-9939-1979-0521879-8

Keywords:
CR-functions,
Levi form,
quadratic maps,
totally indefinite,
CR-extension

Article copyright:
© Copyright 1979
American Mathematical Society