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.
Ahlfors regularity, perimeter measure, sub-Riemannian geometry
Capogna, Luca and Garofalo, Nicola, "Ahlfors Type Estimates For Perimeter Measures In Carnot-carathéodory Spaces" (2006). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.