On regular Stein neighborhoods of a union of two totally real planes in $\mathbb {C}^2$
Volume 117 / 2016
Annales Polonici Mathematici 117 (2016), 1-15
MSC: Primary 32Q28; Secondary 32T15, 54C15.
DOI: 10.4064/ap3754-4-2016
Published online: 10 June 2016
Abstract
We find regular Stein neighborhoods of a union of totally real planes $M=(A+iI)\mathbb {R}^2$ and $N=\mathbb {R}^2$ in $\mathbb {C}^2$, provided that the entries of a real $2 \times 2$ matrix $A$ are sufficiently small. A key step in our proof is a local construction of a suitable function $\rho $ near the origin. The sublevel sets of $\rho $ are strongly Levi pseudoconvex and admit strong deformation retraction to $M\cup N$.
