科研之友
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摘要
We prove that, in general, H-regular surfaces in the Heisenberg group H(1) are not bi-Lipschitz equivalent, to the plane R(2) endowed with the "parabolic" distance which instead is the model space for C(1) surfaces without characteristic points. In Heisenberg groups H(n), 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.
- 出版日期2010
