On uniform large-scale volume growth for the Carnot–Carathéodory metric on unbounded model hypersurfaces in ℂ2

Ethan Dlugie, Aaron Peterson

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider the rate of volume growth of large Carnot–Carathéodory metric balls on a class of unbounded model hypersurfaces in ℂ2. When the hypersurface has a uniform global structure, we show that a metric ball of radius δ ≫ 1 either has volume on the order of δ3 or δ4. We also give necessary and sufficient conditions on the hypersurface to display either behavior.

Original languageEnglish (US)
Pages (from-to)103-118
Number of pages16
JournalInvolve
Volume11
Issue number1
DOIs
StatePublished - 2018

Funding

Dlugie’s work was supported by a grant from the WCAS Undergraduate Research Grant Program, which is administered by Northwestern University’s Weinberg College of Arts and Sciences. The authors thank the referee for many suggestions which improved the quality and clarity of the paper.

Keywords

  • Carnot–Carathéodory metric
  • global behavior
  • volume growth

ASJC Scopus subject areas

  • General Mathematics

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