A Frobenius-Nirenberg theorem with parameter
Complex Variables
2017-11-30 v2 Classical Analysis and ODEs
Abstract
The Newlander-Nirenberg theorem says that a formally integrable complex structure is locally equivalent to the complex structure in the complex Euclidean space. We will show two results about the Newlander-Nirenberg theorem with parameter. The first extends the Newlander-Nirenberg theorem to a parametric version, and its proof yields a sharp regularity result as Webster's proof for the Newlander-Nirenberg theorem. The second concerns a version of Nirenberg's complex Frobenius theorem and its proof yields a result with a mild loss of regularity.
Cite
@article{arxiv.1611.03939,
title = {A Frobenius-Nirenberg theorem with parameter},
author = {Xianghong Gong},
journal= {arXiv preprint arXiv:1611.03939},
year = {2017}
}
Comments
Final version. To appear in J. Reine Angew. Math