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arXiv · 1504.00795

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

Tadej Starčič
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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 $M\cup N$.

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Tadej Starčič. 2015-04-03. On regular Stein neighborhoods of a union of two totally real planes in $\mathbb{C}^2$. https://doi.org/10.4064/ap3754-4-2016

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