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arXiv · 2608.06974

Left-invariant metrics on step-two Carnot groups are uniformly doubling

Cheng Bi·Ye Zhang
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Abstract

We prove that the uniform doubling property holds for left-invariant Riemannian metrics on every step-two Carnot group and the sharp uniform doubling constant is $2^Q$, where $Q$ is the homogeneous dimension. More generally, every such metric satisfies the Bishop--Gromov type estimate.

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Cheng Bi, Ye Zhang. 2026-08-07. Left-invariant metrics on step-two Carnot groups are uniformly doubling. https://arxiv.org/abs/2608.06974

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