Carnot-Carathéodory Metrics in Unbounded Subdomains of ${\mathbb{C}}^2$

Abstract

We introduce a new class of unbounded model subdomains of ${\mathbb{C}}^2$ for the ${\square }_b$ 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-Carathéodory metric induced on the boundary of such domains by the real and imaginary parts of the CR vector field.

Cited by in corpus (1)

• On Uniform Large-Scale Volume Growth for the Carnot-Carathéodory Metric on Unbounded Model Hypersurfaces in ${\mathbb{C}}^2$