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

Keywords

  • Carnot–Carathéodory metric
  • global behavior
  • volume growth

ASJC Scopus subject areas

  • Mathematics(all)

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