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

摘要

We introduce a new class of unbounded model subdomains of $\mathbb{C}^2$ forthe $\Box_b$ problem. Unlike previous finite type models, these domains neednot be bounded by algebraic varieties. In this paper we obtain precise globalestimates for the Carnot-Carath\'eodory metric induced on the boundary of suchdomains by the real and imaginary parts of the CR vector field.