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Journal of Geometric Analysis

, Volume 21, Issue 4, pp 1044–1084 | Cite as

Differentiability of Intrinsic Lipschitz Functions within Heisenberg Groups

  • Bruno FranchiEmail author
  • Raul Serapioni
  • Francesco Serra Cassano
Article

Abstract

We study the notion of intrinsic Lipschitz graphs within Heisenberg groups, focusing our attention on their Hausdorff dimension and on the almost everywhere existence of (geometrically defined) tangent subgroups. In particular, a Rademacher type theorem enables us to prove that previous definitions of rectifiable sets in Heisenberg groups are natural ones.

Keywords

Heisenberg groups Carnot–Carathéodory metric Intrinsic Lipschitz maps Rademacher’s theorem Rectifiability 

Mathematics Subject Classification (2000)

58C20 22E30 

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Copyright information

© Mathematica Josephina, Inc. 2010

Authors and Affiliations

  • Bruno Franchi
    • 1
    Email author
  • Raul Serapioni
    • 2
  • Francesco Serra Cassano
    • 2
  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly
  2. 2.Dipartimento di MatematicaUniversità di TrentoPovo (Trento)Italy

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