Abstract
We prove that, in general, H-regular surfaces in the Heisenberg group H1 are not bi-Lipschitz equivalent to the plane R2 en- dowed with the “parabolic” distance, which instead is the model space for C1 surfaces without characteristic points. In Heisenberg groups Hn, H-regular surfaces can be seen as intrinsic graphs: we show that such parametrizations do not belong to Sobolev classes of metric-space valued maps.
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