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This article is part of the series Harnack's Estimates, Positivity and Local Behavior of Degenerate and Singular Parabolic Equations.

Open Access Research Article

Removable Singularities of -Differential Forms and Quasiregular Mappings

Olli Martio1*, Vladimir Miklyukov2 and Matti Vuorinen3

Author Affiliations

1 Department of Mathematics, University of Helsinki, P.O. Box 68, Helsinki 00014, Finland

2 Department of Mathematics, Volgograd State University, Universitetskii prospect 100, Volgograd 400062, Russia

3 Department of Mathematics, University of Turku, Turku 20014, Finland

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Boundary Value Problems 2007, 2007:061602  doi:10.1155/2007/61602

The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/061602


Received:14 May 2006
Revisions received:6 September 2006
Accepted:20 September 2006
Published:3 December 2006

© 2007 Martio et al.

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.

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

References

  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. 202(1), 73–92 (2002). Publisher Full Text OpenURL

  2. Federer, H: Geometric Measure Theory, Die Grundlehren der mathematischen Wissenschaften,p. xiv+676. Springer, New York (1969)

  3. Heinonen, J, Kilpeläinen, T, Martio, O: Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs,p. vi+363. The Clarendon Press, New York (1993)

  4. Reshetnyak, YuG: Space Mappings with Bounded Distortion, Translations of Mathematical Monographs,p. xvi+362. American Mathematical Society, Rhode Island (1989)

  5. Miklyukov, V: Removable singularities of quasi-conformal mappings in space. Doklady Akademii Nauk SSSR. 188(3), 525–527 (1969)