Solving the $d$ and $\bar\partial$-equation in thin tubes and applications to mappings
Complex Variables
2014-09-16 v2
Abstract
We construct a family of integral kernels for solving the \bar\partial equation with C^k and Holder estimates in thin tubes around totally real submanifolds in complex Eulidean spaces (theorems 1.1 and 3.1). Combining this with the proof of a theorem of Serre we solve the d-equation with estimates for holomorphic forms in such tubes (theorem 5.1). We apply these techniques and a method of Moser to approximate C^k-diffeomorphisms between totally real submanifolds in C^n in the C^k-topology by biholomorphic mappings in tubes, by unimodular and symplectic biholomorphic mappings, and by holomorphic automorphisms of C^n.
Cite
@article{arxiv.math/0003149,
title = {Solving the $d$ and $\bar\partial$-equation in thin tubes and applications to mappings},
author = {Franc Forstneric and Erik Low and Nils Øvrelid},
journal= {arXiv preprint arXiv:math/0003149},
year = {2014}
}
Comments
This is the published version of the paper