The coarea formula for projections of Lipschitz mappings on Carnot groups
Sergey Basalaev
TL;DR
This paper establishes a coarea formula for projections of Lipschitz mappings in Carnot groups, demonstrating equality cases for mappings with finite codistortion and specific cases on the Heisenberg group.
Contribution
It introduces a coarea inequality for Lipschitz mappings in Carnot groups and identifies conditions under which equality holds, advancing geometric measure theory in sub-Riemannian spaces.
Findings
Proved a coarea inequality for Lipschitz mappings in Carnot groups.
Established equality conditions for mappings with finite codistortion.
Demonstrated the formula specifically on the Heisenberg group.
Abstract
A special type of coarea inequality is proved for compositions of intrinsically Lipschitz mappings of Carnot groups with projections along horizontal vector fields. It is proved that the equality is achieved for mappings with finite codistortion and mappings on the Heisenberg group.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Analytic and geometric function theory