Carnot-Carathéodory metrics in unbounded subdomains of ℂ2

Aaron Peterson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)437-447
Number of pages11
JournalArchiv der Mathematik
Volume102
Issue number5
DOIs
StatePublished - 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

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