The Journal of Geometric Analysis

, 16:455

Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces

Authors

  • Luca Capogna
    • Department of MathematicsUniversity of Arkansas
    • Department of MathematicsPurdue University
  • Nicola Garofalo
    • Department of MathematicsUniversity of Arkansas
    • Department of MathematicsPurdue University
Article

DOI: 10.1007/BF02922062

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

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.

Math Subject Classifications

28C1531C4558C35

Key Words and Phrases

Ahlfors regularityperimeter measuresub-Riemannian geometry
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© Mathematica Josephina, Inc. 2006