The Complex Frobenius Theorem for Rough Involutive Structures

Details The Complex Frobenius Theorem for Rough Involutive Structures The Complex Frobenius Theorem for Rough Involutive Structures

2007-10-11

arxiv.org/abs/0710.2316v2

Trans. AMS 359 (2007), 293-322

Mathematics

Differential Geometry

In the two papers by Hill & Taylor, we have adjusted the page height so that the arxiv does not cut off the bottom two lines o

Scientific paper

We establish a version of the complex Frobenius theorem in the context of a complex subbundle S of the complexified tangent bundle of a manifold, having minimal regularity. If the subbundle S defines the structure of a Levi-flat CR-manifold, it suffices that 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 previous recent work of the authors.

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