Tubular neighborhoods in the sub-Riemannian Heisenberg groups Ritoré Cortés, Manuel María Heisenberg group Carnot–Carathéodory distance tubular neighborhoods Distance function Singular set Steiner’s formula 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. 2021-02-19T11:15:37Z 2021-02-19T11:15:37Z 2017-09-20 info:eu-repo/semantics/article Ritoré, M. (2021). Tubular neighborhoods in the sub-Riemannian Heisenberg groups. Advances in Calculus of Variations, 14(1), 1-36. [https://doi.org/10.1515/acv-2017-0011] http://hdl.handle.net/10481/66666 10.1515/acv-2017-0011 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Walter De Gruyter Gmbh