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 03 Feb 2023


Submitted Paper

Inserted: 2 feb 2023
Last Updated: 3 feb 2023

Year: 2023

ArXiv: 2302.00040 PDF
Links: personal homepage


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