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Levi foliations in pseudoconvex boundaries and vector fields that commute approximately with $\bar\partial$


Authors: Emil J. Straube and Marcel K. Sucheston
Journal: Trans. Amer. Math. Soc. 355 (2003), 143-154
MSC (2000): Primary 32W05, 32T99; Secondary 53C12
DOI: https://doi.org/10.1090/S0002-9947-02-03133-1
Published electronically: September 6, 2002
MathSciNet review: 1928081
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Abstract: Boas and Straube proved a general sufficient condition for global regularity of the $\bar\partial$-Neumann problem in terms of families of vector fields that commute approximately with $\bar\partial$. In this paper, we study the existence of these vector fields on a compact subset of the boundary whose interior is foliated by complex manifolds. This question turns out to be closely related to properties of interest from the point of view of foliation theory.


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Additional Information

Emil J. Straube
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: straube@math.tamu.edu

Marcel K. Sucheston
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368

DOI: https://doi.org/10.1090/S0002-9947-02-03133-1
Received by editor(s): September 15, 2000
Published electronically: September 6, 2002
Additional Notes: Research supported in part by NSF grant DMS-9801539
Marcel K. Sucheston died tragically on April 24, 2000. The surviving author dedicates this paper to his memory
Article copyright: © Copyright 2002 American Mathematical Society

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