# John and uniform domains in generalized Siegel boundaries

created by monti on 07 Nov 2018

[BibTeX]

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.