Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces |
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| Authors: | Luca Capogna Nicola Garofalo |
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| Institution: | 1. Department of Mathematics, University of Arkansas, 72701, Fayetteville, AR
2. Department of Mathematics, Purdue University, 47907, West Lafayette, IN
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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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