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Ahlfors Type Estimates For Perimeter Measures In Carnot-Carathéodory Spaces, Luca Capogna, Nicola Garofalo
Ahlfors Type Estimates For Perimeter Measures In Carnot-Carathéodory Spaces, Luca Capogna, Nicola Garofalo
Mathematics Sciences: Faculty Publications
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.