Left-invariant metrics on step-two Carnot groups are uniformly doubling
Cheng Bi, Ye Zhang
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 2Q, where Q is the homogeneous dimension. More generally, every such metric satisfies the Bishop--Gromov type estimate.
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