arXiv: Metric Geometry | 2019
Estimates on the Markov Convexity of Carnot Groups
Abstract
We show that every graded nilpotent Lie group $G$ of step $r$ equipped with a left-invariant, homogeneous metric is Markov $p$-convex for all $p \\in [2r,\\infty)$. We also show that this is sharp whenever $G$ is a Carnot group with $r \\leq 3$ or a model filiform group; such groups are not Markov $p$-convex for any $p \\in (0,2r)$. This continues a line of research started by Li who proved this sharp result when $G$ is the Heisenberg group.