The Journal of Geometric Analysis

, 16:455

Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces

  • Luca Capogna
  • Nicola Garofalo

DOI: 10.1007/BF02922062

Cite this article as:
Capogna, L. & Garofalo, N. J Geom Anal (2006) 16: 455. doi:10.1007/BF02922062


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.

Math Subject Classifications

28C15 31C45 58C35 

Key Words and Phrases

Ahlfors regularity perimeter measure sub-Riemannian geometry 

Copyright information

© Mathematica Josephina, Inc. 2006

Authors and Affiliations

  • Luca Capogna
    • 1
    • 2
  • Nicola Garofalo
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of ArkansasFayetteville
  2. 2.Department of MathematicsPurdue UniversityWest Lafayette

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