Calculus of Variations and Geometric Measure Theory

F. Corni - V. Magnani

Area of intrinsic graphs in homogeneous groups

created by magnani on 16 Nov 2023


Submitted Paper

Inserted: 16 nov 2023
Last Updated: 16 nov 2023

Year: 2023

ArXiv: 2311.06638 PDF


We establish an area formula for computing the spherical measure of an intrinsic graph of any codimension in an arbitrary homogeneous group. Our approach only assumes that the map generating the intrinsic graph is continuously intrinsically differentiable. The important novelty lies in the notion of Jacobian, which is built by the auxiliary Euclidean distance. The introduction of this Jacobian allows the spherical factor to appear in the area formula and enables explicit computations.

Keywords: area formula, intrinsic graph, spherical measure, homogeneous group, homogeneous distance, intrinsic differentiability, spherical factor, Federer density