The complex Frobenius theorem for rough involutive structures

Hill, C.; Taylor, Michael

doi:10.1090/S0002-9947-06-04067-0

The complex Frobenius theorem for rough involutive structures
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by C. Denson Hill and Michael Taylor PDF

Trans. Amer. Math. Soc. 359 (2007), 293-322 Request permission

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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