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arXiv · 1608.01952

On Uniform Large-Scale Volume Growth for the Carnot-Carath\'eodory Metric on Unbounded Model Hypersurfaces in $\mathbb{C}^2$

Ethan Dlugie·Aaron Peterson
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Abstract

We consider the rate of volume growth of large Carnot-Carath\'eodory metric balls on a class of unbounded model hypersurfaces in $\mathbb{C}^2$. When the hypersurface has a uniform global structure, we show that a metric ball of radius $\delta \gg 1$ either has volume on the order of $\delta^3$ or $\delta^4$. We also give necessary and sufficient conditions on the hypersurface to display either behavior.

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Ethan Dlugie, Aaron Peterson. 2016-08-05. On Uniform Large-Scale Volume Growth for the Carnot-Carath\'eodory Metric on Unbounded Model Hypersurfaces in $\mathbb{C}^2$. https://doi.org/10.2140/involve.2018.11.103

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