Carnot-Carathéodory metrics in unbounded subdomains of ℂ2

Aaron Peterson

doi:10.1007/s00013-014-0646-0

Carnot-Carathéodory metrics in unbounded subdomains of ℂ²

Aaron Peterson^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We introduce a new class of unbounded model subdomains of ℂ² for the {dashed fence}_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.

Original language	English (US)
Pages (from-to)	437-447
Number of pages	11
Journal	Archiv der Mathematik
Volume	102
Issue number	5
DOIs	https://doi.org/10.1007/s00013-014-0646-0
State	Published - May 2014

Funding

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.

Keywords

Carnot-Carathéodory metrics
Global behavior

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00013-014-0646-0

Cite this

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title = "Carnot-Carath{\'e}odory metrics in unbounded subdomains of ℂ2",

abstract = "We introduce a new class of unbounded model subdomains of ℂ2 for the {dashed fence}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{\'e}odory metric induced on the boundary of such domains by the real and imaginary parts of the CR vector field.",

keywords = "Carnot-Carath{\'e}odory metrics, Global behavior",

author = "Aaron Peterson",

note = "Funding Information: 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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N2 - We introduce a new class of unbounded model subdomains of ℂ2 for the {dashed fence}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.

AB - We introduce a new class of unbounded model subdomains of ℂ2 for the {dashed fence}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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KW - Global behavior

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