The d-bar-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in CP^n with n>= 3
Differential Geometry
2007-05-23 v2 Complex Variables
Abstract
A Lipschitz hypersurface is a hypersurface which locally is the graph of a Lipschitz function. A Lipschitz (or C^1) hypersurface is said to be Levi-flat if it is locally foliated by complex manifolds of complex dimension (n-1). We shall prove that there exist no Lipschitz Levi-flat hypersurfaces in CP^n with n >= 3. Our new estimates on the d-bar-Cauchy problems are different from the earlier Siu's integral kernal method.
Cite
@article{arxiv.math/0604112,
title = {The d-bar-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in CP^n with n>= 3},
author = {Jianguo Cao and Mei-Chi Shaw},
journal= {arXiv preprint arXiv:math/0604112},
year = {2007}
}