The Journal of Geometric Analysis
We study the relationship between the geometry of hypersurfaces in a Carnot-Carathéodory (CC) space and the Ahlfors regularity of the corresponding perimeter measure. To this end we establish comparison theorems for perimeter estimates between an hypersurface and its tangent space, and between a CC geometry and its “tangent” Carnot group structure.
Capogna, L. & Garofalo, N. (2006). Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces. The Journal of Geometric Analysis, 16(3), 455-497. https://doi.org/10.1007/BF02922062
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This is a pre-print of an article published in The Journal of Geometric Analysis. The final authenticated version is available online at: https://doi.org/10.1007/BF02922062