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Smoothness of Boundaries of Regular Sets

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Abstract

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

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Acknowledgements

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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Authors and Affiliations

  1. CMAF, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016, Lisboa, Portugal

    Pedro Duarte

  2. CMAT, Departamento de Matemática e Aplicações, Universidade do Minho, Campus de Gualtar, 4700-057, Braga, Portugal

    Maria Joana Torres

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  1. Pedro Duarte
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  2. Maria Joana Torres
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Correspondence to Maria Joana Torres.

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Duarte, P., Torres, M.J. Smoothness of Boundaries of Regular Sets. J Math Imaging Vis 48, 106–113 (2014). https://doi.org/10.1007/s10851-012-0397-0

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  • DOI: https://doi.org/10.1007/s10851-012-0397-0

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