Calculus of Variations and Geometric Measure Theory

D. Barilari - T. Bossio

Steiner and tube formulae in 3D contact sub-Riemannian geometry

created by barilari on 03 Feb 2023



Inserted: 3 feb 2023
Last Updated: 3 feb 2023

Year: 2023

ArXiv: 2302.01256 PDF


We prove a Steiner formula for regular surfaces with no characteristic points in 3D contact sub-Riemannian manifolds endowed with an arbitrary smooth volume. The formula we obtain, which is equivalent to a half-tube formula, is of local nature. It can thus be applied to any surface in a region not containing characteristic points. We provide a geometrical interpretation of the coefficients appearing in the expansion, and compute them on some relevant examples in three-dimensional sub-Riemannian model spaces. These results generalize those obtained in and arXiv:1703.01592v3 for the Heisenberg group.