Characterizations of intrinsic rectifiability in Heisenberg groups
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 9 (2010) no. 4, p. 687-723
We define rectifiable sets in the Heisenberg groups as countable unions of Lipschitz images of subsets of a Euclidean space, in the case of low-dimensional sets, or as countable unions of subsets of intrinsic C 1 surfaces, in the case of low-codimensional sets. We characterize both low-dimensional rectifiable sets and low codimensional rectifiable sets with positive lower density, in terms of almost everywhere existence of approximate tangent subgroups or of tangent measures.
Classification:  28A75,  28C10
@article{ASNSP_2010_5_9_4_687_0,
     author = {Mattila, Pertti and Serapioni, Raul and Serra Cassano, Francesco},
     title = {Characterizations of intrinsic rectifiability in Heisenberg groups},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 9},
     number = {4},
     year = {2010},
     pages = {687-723},
     zbl = {1229.28004},
     mrnumber = {2789472},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2010_5_9_4_687_0}
}
Mattila, Pertti; Serapioni, Raul; Serra Cassano, Francesco. Characterizations of intrinsic rectifiability in Heisenberg groups. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 9 (2010) no. 4, pp. 687-723. http://www.numdam.org/item/ASNSP_2010_5_9_4_687_0/

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