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Seminar "Complex analysis in several variables" (Vitushkin Seminar)
March 13, 2019 16:45, Moscow, Moscow State University, Room 13-06


On the hyperbolicity of tube domains in ${\mathbb C}^2$

A. V. Isaev

Abstract: We will discuss the problem of finding an easily verifiable criterion for the Kobayashi-hyperbolicity of tube domains in ${\mathbb C}^2$. The problem naturally splits into two cases: (1) the envelope of holomorphy of the domain is strictly less than ${\mathbb C}^2$, (2) the envelope of holomorphy of the domain is all of ${\mathbb C}^2$. Mostly, we will be interested in the first case. In this situation one can assume that the base of the tube domain lies in the upper half-plane. Surprisingly, even in this apparently simple case there is no easily verifiable criterion for hyperbolicity. In the talk, we will discuss known necessary and sufficient conditions.


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