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On uniform
large-scale volume growth for the Carnot–Carathéodory metric
on unbounded model hypersurfaces in $\mathbb{C}^2$
Ethan Dlugie and Aaron Peterson
Vol. 11 (2018), No. 1, 103–118
DOI: 10.2140/involve.2018.11.103
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Abstract |
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We consider the rate of volume growth of large Carnot–Carathéodory metric balls on a class of unbounded model hypersurfaces in . When the hypersurface has a uniform global structure, we show that a metric ball of radius either has volume on the order of or . We also give necessary and sufficient conditions on the hypersurface to display either behavior. |
Keywords
Carnot–Carathéodory metric, global behavior, volume growth
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Mathematical Subject Classification 2010
Primary: 53C17
Secondary: 32V15, 43A85
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Milestones
Received: 5 August 2016
Revised: 11 December 2016
Accepted: 3 January 2017
Published: 17 July 2017
Communicated by Michael Dorff
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Authors |
| Ethan Dlugie | |
| Department of Mathematics Northwestern University 2033 Sheridan Road Evanston, IL 60208 United States |
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| Aaron Peterson | |
| Department of Mathematics Northwestern University 2033 Sheridan Road Evanston, IL 60208 United States |
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