Measure of curves in graded groups
Riikka Korte, Valentino Magnani
TL;DR
This paper derives an area-type formula for the intrinsic spherical Hausdorff measure of regular curves within any graded group, advancing geometric measure theory in sub-Riemannian geometry.
Contribution
It introduces a general formula for measuring regular curves in graded groups, extending previous results to broader geometric contexts.
Findings
Established an area-type formula for intrinsic measures
Applied the formula to regular curves in graded groups
Enhanced understanding of geometric measures in sub-Riemannian spaces
Abstract
We establish an area-type formula for the intrinsic spherical Hausdorff measure of every regular curve embedded in an arbitrary graded group.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Mathematical Dynamics and Fractals · Geometry and complex manifolds