, Volume 16, Issue 3, pp 455-497

Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces

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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.