The Complex Frobenius Theorem for Rough Involutive Structures
Differential Geometry
2007-11-08 v2 Analysis of PDEs
Complex Variables
Abstract
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.
Cite
@article{arxiv.0710.2316,
title = {The Complex Frobenius Theorem for Rough Involutive Structures},
author = {C. Denson Hill and Michael Taylor},
journal= {arXiv preprint arXiv:0710.2316},
year = {2007}
}
Comments
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 of each page, being unable to digest our amstex