Inserted: 2 feb 2023
Last Updated: 3 feb 2023
We prove an integral formula for the spherical measure of hypersurfaces in equiregular sub-Riemannian manifolds. Among various technical tools, we establish a general criterion for the uniform convergence of parametrized sub-Riemannian distances, and local uniform asymptotics for the diameter of small metric balls.
Keywords: Hausdorff measure, sub-Riemannian distance, Set of finite perimeter, Sub-Riemannian manifold, Caccioppoli set