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Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Arkansas, 72701, Fayetteville, AR

    Luca Capogna & Nicola Garofalo

  2. Department of Mathematics, Purdue University, 47907, West Lafayette, IN

    Luca Capogna & Nicola Garofalo

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  1. Luca Capogna
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  2. Nicola Garofalo
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Capogna, L., Garofalo, N. Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces. J Geom Anal 16, 455–497 (2006). https://doi.org/10.1007/BF02922062

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