We find regular Stein neighborhoods of a union of totally real planes M = (A+iI)ℝ² and N = ℝ² in ℂ², provided that the entries of a real 2 × 2 matrix A are sufficiently small. A key step in our proof is a local construction of a suitable function ρ near the origin. The sublevel sets of ρ are strongly Levi pseudoconvex and admit strong deformation retraction to M ∪ N.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap3754-4-2016,
author = {Tadej Star\v ci\v c},
title = {On regular Stein neighborhoods of a union of two totally real planes in $\mathbb{C}$$^2$},
journal = {Annales Polonici Mathematici},
volume = {116},
year = {2016},
pages = {1-15},
zbl = {06602753},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3754-4-2016}
}
Tadej Starčič. On regular Stein neighborhoods of a union of two totally real planes in ℂ². Annales Polonici Mathematici, Tome 116 (2016) pp. 1-15. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3754-4-2016/