@misc{10481/66666,
year = {2017},
month = {9},
url = {http://hdl.handle.net/10481/66666},
abstract = {In the present paper we consider the Carnot–Carathéodory distance δE to a closed set E in the
sub-RiemannianHeisenberg groupsℍn, n ⩾ 1. Theℍ-regularity of δE is proved under mild conditions involving
a general notion of singular points. In case E is a Euclidean Ck submanifold, k ⩾ 2, we prove that δE is Ck
out of the singular set. Explicit expressions for the volume of the tubular neighborhood when the boundary
of E is of class C2 are obtained, out of the singular set, in terms of the horizontal principal curvatures of ∂E
and of the function ⟨N, T⟩/|Nh| and its tangent derivatives.},
organization = {European Union (EU)

Spanish Government

MTM2007-61919
MTM2013-48371-C2-1-P},
organization = {Junta de Andalucía

FQM-325},
publisher = {Walter De Gruyter Gmbh},
keywords = {Heisenberg group},
keywords = {Carnot–Carathéodory distance},
keywords = {tubular neighborhoods},
keywords = {Distance function},
keywords = {Singular set},
keywords = {Steiner’s formula},
title = {Tubular neighborhoods in the sub-Riemannian Heisenberg groups},
doi = {10.1515/acv-2017-0011},
author = {Ritoré Cortés, Manuel María},
}