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Mathematische Annalen

, Volume 342, Issue 4, pp 727–748 | Cite as

Outer Minkowski content for some classes of closed sets

  • Luigi AmbrosioEmail author
  • Andrea Colesanti
  • Elena Villa
Article

Abstract

We find conditions ensuring the existence of the outer Minkowski content for d-dimensional closed sets in \({\mathbb{R}^d}\) , in connection with regularity properties of their boundaries. Moreover, we provide a class of sets (including all sufficiently regular sets) stable under finite unions for which the outer Minkowski content exists. It follows, in particular, that finite unions of sets with Lipschitz boundary and a type of sets with positive reach belong to this class.

Mathematics Subject Classification (2000)

28A75 49Q15 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di FirenzeFirenzeItaly
  3. 3.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanItaly

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