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 language | English (US) |
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Pages (from-to) | 103-118 |
Number of pages | 16 |
Journal | Involve |
Volume | 11 |
Issue number | 1 |
DOIs | |
State | Published - 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