On regular Stein neighborhoods of a union of two totally real planes in ${\mathbb{C}}^2$

Abstract

In this paper we find regular Stein neighborhoods for 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 $M\cup N$.

Cited by in corpus (1)

• On regular Stein neighborhoods of a union of two maximal totally real subspaces in ${\mathbb{C}}^n$