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Abstract and Applied Analysis
Volume 2010, Article ID 646392, 29 pages
Research Article

Ahlfors Theorems for Differential Forms

1Department of Mathematics and Statistics, University of Helsinki, 00014 Helsinki, Finland
2Mathematics Department, Volgograd State University, 2 Prodolnaya 30, Volgograd 400062, Russia
3Department of Mathematics, University of Turku, 20014 Turku, Finland

Received 11 September 2010; Accepted 18 October 2010

Academic Editor: Nikolaos Papageorgiou

Copyright © 2010 O. 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.

Linked References

  1. D. Franke, O. Martio, V. M. Miklyukov, M. Vuorinen, and R. Wisk, “Quasiregular mappings and 𝒲𝒯-classes of differential forms on Riemannian manifolds,” Pacific Journal of Mathematics, vol. 202, no. 1, pp. 73–92, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  2. G. D. Suvorov, Semeistva ploskikh topologicheskikh otobrazhenii, Izdat. Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk, Russia, 1965.
  3. V. M. Kesel'man, “Riemannian manifolds of α-parabolic type,” Izvestiya Vysshikh Uchebnykh Zavedeniĭ. Matematika, no. 4, pp. 81–83, 1985. View at Google Scholar
  4. V. M. Miklyukov, “Conditions of parabolic and hyperbolic type of boundary sets of surfaces,” Russian Mat. Izv., Ser. Mat., vol. 60, no. 4, pp. 111–158, 1996. View at Google Scholar
  5. J. Heinonen, T. Kilpeläinen, and O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs, The Clarendon Press, New York, NY, USA, 1993.
  6. B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Sovremennaya Geometriya: Metody i prilozheniya, “Nauka”, Moscow, Russia, 1979. View at Zentralblatt MATH
  7. H. Federer, Geometric Measure Theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer, New York, NY, USA, 1969. View at Zentralblatt MATH
  8. V. A. Klyachin, “Some geometric estimates of the constant in Poincare’s inequality on the geodesic spheres in Riemannian manifolds,” Reports of the Dep. of Math., Preprint 181, University of Helsinki, pp. 1–7, 1998.
  9. O. Martio, V. M. Miklyukov, and M. Vuorinen, “Wiman and Arima theorems for quasiregular mappings,” Journal of Inequalities and Applications, vol. 2010, Article ID 604217, 29 pages, 2010. View at Publisher · View at Google Scholar
  10. W. K. Hayman and P. B. Kennedy, Subharmonic Functions I., Academic Press, New York, NY, USA, 1976.
  11. W. K. Hayman and P. B. Kennedy, Subharmonic Functions II, Academic Press, New York, NY, USA, 1989.
  12. V. M. Mikljukov, “Asymptotic properties of subsolutions of quasilinear equations of elliptic type and mappings with bounded distortion,” Matematicheskiĭ Sbornik. Novaya Seriya, vol. 111, no. 1, pp. 42–66, 1980, English translation, Mathematics of the USSR-Sbornik, vol. 39, pp. 37–60, 1981. View at Google Scholar