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–Carathéodory metric induced on the boundary of such domains by the real and imaginary parts of the CR vector field.
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This work was supported in part by NSF Grant No. 1147523-RTG: Analysis and Applications at the University of Wisconsin-Madison. The author would like to thank Professor Alexander Nagel for his support throughout this project, and Professor Brian Street for helpful conversations. The author would also like to thank the anonymous reviewer for their helpful comments.
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Peterson, A. Carnot–Carathéodory metrics in unbounded subdomains of \({{\mathbb{C}}^2}\) . Arch. Math. 102, 437–447 (2014). https://doi.org/10.1007/s00013-014-0646-0
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DOI: https://doi.org/10.1007/s00013-014-0646-0