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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The complex Frobenius theorem for rough involutive structures


Authors: C. Denson Hill and Michael Taylor
Journal: Trans. Amer. Math. Soc. 359 (2007), 293-322
MSC (2000): Primary 35N10
Published electronically: August 16, 2006
MathSciNet review: 2247892
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Abstract: We establish a version of the complex Frobenius theorem in the context of a complex subbundle $ \mathcal{S}$ of the complexified tangent bundle of a manifold having minimal regularity. If the subbundle $ \mathcal{S}$ defines the structure of a Levi-flat CR-manifold, it suffices that $ \mathcal{S}$ be Lipschitz for our results to apply. A principal tool in the analysis is a precise version of the Newlander-Nirenberg theorem with parameters, for integrable almost complex structures with minimal regularity, which builds on recent work of the authors.


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Additional Information

C. Denson Hill
Affiliation: Department of Mathematics, Stony Brook University, Stony Brook, New York 11794
Email: dhill@math.sunysb.edu

Michael Taylor
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599
Email: met@math.unc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04067-0
PII: S 0002-9947(06)04067-0
Received by editor(s): November 4, 2004
Published electronically: August 16, 2006
Additional Notes: The second author was partially supported by NSF grant DMS-0139726
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.