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arXiv · 1805.06791

John and uniform domains in generalized Siegel boundaries

Roberto Monti·Daniele Morbidelli
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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 $(x,y,t)= (z,t)\in\mathbb{R}^3=\mathbb{C}\times\mathbb{R}$, we give a condition on a bounded domain $Ω\subset\mathbb{R}^3$ which ensures that $Ω$ is an $(ε,δ)$-domain for the Carnot-Carathéodory metric. We also analyze the Ahlfors regularity of the natural surface measure induced at the boundary by the vector fields.

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Roberto Monti, Daniele Morbidelli. 2019-08-02. John and uniform domains in generalized Siegel boundaries. https://doi.org/10.1007/s11118-019-09792-w

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