Document Type
Article
Publication Date
12-1-2006
Publication Title
Journal of Geometric Analysis
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.
Keywords
Ahlfors regularity, perimeter measure, sub-Riemannian geometry
Volume
16
Issue
3
First Page
455
Last Page
497
DOI
10.1007/BF02922062
ISSN
10506926
Recommended Citation
Capogna, Luca and Garofalo, Nicola, "Ahlfors Type Estimates For Perimeter Measures In Carnot-carathéodory Spaces" (2006). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/144
Comments
Peer reviewed accepted manuscript.