*Submitted Paper*

**Inserted:** 7 nov 2018

**Last Updated:** 7 nov 2018

**Year:** 2018

**Abstract:**

Given the pair of vector fields

$X=\partial_x+z ^{2m}y\partial_t$

and

$Y=\partial_y-z^{2m}x \partial_t$

where $(x,y,t)= (z,t)\in\R^3=\C\times\R$, we give a condition on a bounded domain $\Omega\subset\R^3$ which ensures that $\Omega$ is an $(\epsilon,\delta)$-domain for the Carnot-Carath\'eodory metric. We also analyze the Ahlfors regularity of the natural surface measure induced on $ \partial \Omega$ by the vector fields.

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