On uniform large-scale volume growth for the Carnot–Carathéodory metric on unbounded model hypersurfaces in ℂ2
On uniform large-scale volume growth for the Carnot–Carathéodory metric on unbounded model hypersurfaces in ℂ2
复制标题
ℂ2 中无界模型超曲面上卡诺-卡拉西奥多里度量的均匀大规模体积增长
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发表时间：
2016
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通讯作者：
Aaron Peterson
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作者：
Ethan Dlugie;Aaron Peterson
本文研究了$mathbb{C}^2 $中一类无界模型超曲面上大Carnot-Carath'eodory度规球的体积增长率。当超曲面具有一致的整体结构时，我们证明了半径为$delta gg 1$的度量球的体积为$delta ^3 $或$delta ^4 $。我们也给出了超曲面上的充要条件，以显示任何行为。
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.