Calculus of Variations and Geometric Measure Theory

S. Don - V. Magnani

Surface measure on, and the local geometry of, sub-Riemannian manifolds

created by magnani on 02 Feb 2023
modified on 19 Nov 2023


Published Paper

Inserted: 2 feb 2023
Last Updated: 19 nov 2023

Journal: Calc. Var. Partial Differential Equations
Volume: 62
Number: 254
Pages: 42
Year: 2023
Links: freely available


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, spherical measure, Set of finite perimeter, Sub-Riemannian manifold, spherical factor, Caccioppolsub-Riemannian distancei set, measure-theoretic area formula