Abstract
In the Heisenberg group, we prove that the boundary of sets with finite \({\mathbb H}\)-perimeter and having a bound on the measure theoretic normal is an \({\mathbb H}\)-Lipschitz graph. Then we show that if the normal is, on the boundary, the restriction of a continuous mapping, then the boundary is an \({\mathbb H}\)-regular surface.
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R.M. supported by GNAMPA (MIUR, Italy), University of Padova, Mathematics Institute of Bern.
D.V. supported by GALA project of the Sixth Framework Programme of European Community, GNAMPA of MIUR (Italy) and University of Padova.
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Monti, R., Vittone, D. Sets with finite \({\mathbb H}\)-perimeter and controlled normal. Math. Z. 270, 351–367 (2012). https://doi.org/10.1007/s00209-010-0801-7
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DOI: https://doi.org/10.1007/s00209-010-0801-7