Carnot-Carath\'eodory Metrics in Unbounded Subdomains of $\mathbb{C}^2$

Abstract

We introduce a new class of unbounded model subdomains of $\mathbb{C}^2$ for the $\Box_b$ problem. Unlike previous finite type models, these domains need not be bounded by algebraic varieties. In this paper we obtain precise global estimates for the Carnot-Carath\'eodory metric induced on the boundary of such domains by the real and imaginary parts of the CR vector field.