Area formula for regular submanifolds of low codimension in Heisenberg groups

2020/02/04 by Francesca Corni, Corni, Francesca, Valentino Magnani +1 · 1 citation
Computer Science · Mathematics · #Geometric Analysis and Curvature Flows #Topological and Geometric Data Analysis #advanced mathematical theories #math.MG

paper · pdf · doi:10.48550/arxiv.2002.01433

27 pages

arxiv created 2021/06/09 · arxiv updated 2021/06/10

Abstract

We establish an area formula for the spherical measure of intrinsically regular submanifolds of low codimension in Heisenberg groups. The spherical measure is computed with respect to an arbitrary homogeneous distance. Among the arguments of the proof, we point out the differentiability properties of intrinsic graphs and a chain rule for intrinsic differentiable functions.

Cited by

• Submanifolds with boundary in sub-Riemannian Heisenberg Groups

Related

• Intrinsic Regular Surfaces of low codimension in Heisenberg groups
• Area of intrinsic graphs in homogeneous groups
• Blow-up of regular submanifolds in Heisenberg groups and applications
• Towards a theory of area in homogeneous groups
• Cauchy surface area formula in the Heisenberg groups