Removable Singularities of -Differential Forms and Quasiregular Mappings

  • Olli Martio1Email author,

    Affiliated with

    • Vladimir Miklyukov2 and

      Affiliated with

      • Matti Vuorinen3

        Affiliated with

        Boundary Value Problems20062007:061602

        DOI: 10.1155/2007/61602

        Received: 14 May 2006

        Accepted: 20 September 2006

        Published: 3 December 2006


        A theorem on removable singularities of -differential forms is proved and applied to quasiregular mappings.


        Authors’ Affiliations

        Department of Mathematics, University of Helsinki
        Department of Mathematics, Volgograd State University
        Department of Mathematics, University of Turku


        1. Franke D, Martio O, Miklyukov V, Vuorinen M, Wisk R: Quasiregular mappings and-classes of differential forms on Riemannian manifolds. Pacific Journal of Mathematics 2002,202(1):73–92. 10.2140/pjm.2002.202.73MATHMathSciNetView Article
        2. Federer H: Geometric Measure Theory, Die Grundlehren der mathematischen Wissenschaften. Volume 153. Springer, New York; 1969:xiv+676.
        3. Heinonen J, Kilpeläinen T, Martio O: Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs. The Clarendon Press, New York; 1993:vi+363.
        4. Reshetnyak YuG: Space Mappings with Bounded Distortion, Translations of Mathematical Monographs. Volume 73. American Mathematical Society, Rhode Island; 1989:xvi+362.
        5. Miklyukov V: Removable singularities of quasi-conformal mappings in space. Doklady Akademii Nauk SSSR 1969,188(3):525–527.MATHMathSciNet


        © Olli Martio et al. 2007

        This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.