Journal of Mathematical Imaging and Vision

, Volume 48, Issue 1, pp 106–113 | Cite as

Smoothness of Boundaries of Regular Sets

  • Pedro Duarte
  • Maria Joana TorresEmail author


We prove that the boundary of an r-regular set is a codimension one manifold of class C 1.


r-regularity C1-boundary Lipschitz projection Euclidean distance 



PD was supported by “Fundação para a Ciência e a Tecnologia” through the Program POCI 2010 and the Project “Randomness in Deterministic Dynamical Systems and Applications” (PTDC-MAT-105448-2008). MJT was partially financed by FEDER Funds through “Programa Operacional Factores de Competitividade—COMPETE” and by Portuguese Funds through FCT—“Fundação para a Ciência e a Tecnologia”, within the Project PEst-C/MAT/UI0013/2011.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.CMAF, Departamento de Matemática, Faculdade de CiênciasUniversidade de LisboaLisboaPortugal
  2. 2.CMAT, Departamento de Matemática e AplicaçõesUniversidade do MinhoBragaPortugal

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