Skip to main content
SpringerLink
Log in

Topological properties of quasiregular mappings

  • Conference paper
  • First Online:
Quasiconformal Space Mappings

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1508))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. AGARD and A. MARDEN: A removable singularity theorem for local homeomorphisms, Indiana Math. J. 20 (1970), 455–461.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. V. CHERNAVSKIǏ: Finite-to-one open mappings of manifolds. (Russian), Mat. Sb. 65 (1964), 357–369.

    MathSciNet  Google Scholar 

  3. A. V. CHERNAVSKIǏ: Remarks on the paper “On finite-to-one mappings of manifolds”, (Russian), Mat. Sb. 66 (1965), 471–472.

    MathSciNet  Google Scholar 

  4. P. T. CHURCH and E. HEMMINGSEN: Light open maps on n-manifolds, Duke Math. J. 27 (1960), 527–536.

    Article  MathSciNet  MATH  Google Scholar 

  5. P. T. CHURCH and J. G. TIMOURIAN: Differentiable maps with small critical set or critical set image, Indiana Univ. Math. J. 27 (1978), 953–971.

    Article  MathSciNet  MATH  Google Scholar 

  6. V. M. GOL’DSHTEIN: The behavior of mappings with bounded distortion when the coefficient of distortion is close to unity, Sibirsk. Math. Zh. 12 (1971), 900–906.

    Article  Google Scholar 

  7. T. IWANIEC: p-harmonic tensors and quasiregular mappings, Ann. Math. (to appear).

    Google Scholar 

  8. T. IWANIEC and G. MARTIN: Quasiregular mappings in even dimensions, Acta Math. (to appear).

    Google Scholar 

  9. P. JÄRVI: On the behavior of quasiregular mappings in the neighborhood of an isolated singularity, Ann. Acad. Sci. Fenn. Ser. A I Math. 15 (1990), 341–353.

    Article  MathSciNet  MATH  Google Scholar 

  10. P. JÄRVI and M. VUORINEN: Self-similar Cantor sets and quasiregular mappings, J. Reine Angew. Math. 424 (1992), 31–45.

    MathSciNet  MATH  Google Scholar 

  11. P. KOSKELA and O. MARTIO: Removability theorems for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I Math. 15 (1990), 381–399.

    Article  MathSciNet  MATH  Google Scholar 

  12. O. MARTIO: A capacity inequality for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 474 (1970), 1–18.

    MathSciNet  MATH  Google Scholar 

  13. O. MARTIO: On k-periodic quasiregular mappings in R n, Ann. Acad. Sci. Fenn. Ser. A I Math. 1 (1975), 207–220.

    Article  MathSciNet  MATH  Google Scholar 

  14. O. MARTIO and S. RICKMAN: Boundary behavior of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 507 (1972), 1–17.

    MathSciNet  MATH  Google Scholar 

  15. O. MARTIO and S. RICKMAN: Measure properties of the branch set and its image of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 541 (1973), 1–16.

    MathSciNet  MATH  Google Scholar 

  16. O. MARTIO, S. RICKMAN, and J. VÄISÄLÄ: Definitions for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 448 (1969), 1–40.

    MathSciNet  MATH  Google Scholar 

  17. O. MARTIO, S. RICKMAN, and J. VÄISÄLÄ: Distortion and singularities of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 465 (1970), 1–13.

    MathSciNet  MATH  Google Scholar 

  18. O. MARTIO, S. RICKMAN, and VÄISÄLÄ: Topological and metric properties of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 488 (1971), 1–31.

    MathSciNet  MATH  Google Scholar 

  19. O. MARTIO and J. SARVAS: Injectivity theorems in plane and space, Ann. Acad. Sci. Fenn. Ser. A I Math. 4 (1978/1979), 383–401.

    Article  MathSciNet  MATH  Google Scholar 

  20. O. MARTIO and U. SREBRO: Periodic quasimeromorphic mappings in R n, J. Analyse Math. 28 (1975), 20–40.

    Article  MATH  Google Scholar 

  21. O. MARTIO and U. SREBRO: Automorphic quasimeromorphic mappings in R n, Acta Math. 135 (1975), 221–247.

    Article  MathSciNet  MATH  Google Scholar 

  22. O. MARTIO and U. SREBRO: On the existence of automorphic quasimeromorphic mappings in R n, Ann. Acad. Sci. Fenn. Ser. A I Math. 3 (1977), 123–130.

    Article  MathSciNet  MATH  Google Scholar 

  23. O. MARTIO and U. SREBRO: Universal radius of injectivity for locally quasiconformal mappings, Israel J. Math. 29 (1978), 17–23.

    Article  MathSciNet  MATH  Google Scholar 

  24. O. MARTIO and U. SREBRO: On the local behavior of quasiregular maps and branched covering maps, J. Analyse Math. 36 (1979), 198–212.

    Article  MathSciNet  MATH  Google Scholar 

  25. O. MARTIO and U. SREBRO: To appear.

    Google Scholar 

  26. R. NEVANLINNA: Analytic Functions, Die Grundlehren der math. Wissenschaften Vol. 162, Springer-Verlag, Berlin-Heidelberg-New York, 1970.

    Book  MATH  Google Scholar 

  27. K. PELTONEN: On the existence of quasiregular mappings, Manuscript, (1988).

    Google Scholar 

  28. YU. G. RESHETNYAK: Space mappings with bounded distortion (Russian), Sibirsk. Mat. Zh. 8 (1967), 626–659.

    Google Scholar 

  29. YU. G. RESHETNYAK: Space Mappings with Bounded Distortion, Translations of Mathematical Monographs Vol. 73, Amer. Math. Soc. Providence, R.I., 1989.

    Google Scholar 

  30. S. RICKMAN: Quasiregular Mappings, Proc. Romanian-Finnish Seminar on Teichmüller spaces and quasiconformal mappings, Brasov, (1969), 261–271.

    Google Scholar 

  31. S. RICKMAN: On the number of omitted values of entire quasiregular mappings, J. Analyse Math. 37 (1980), 100–117.

    Article  MathSciNet  MATH  Google Scholar 

  32. S. RICKMAN: Asymptotic values and angular limits of quasiregular mappings of a ball, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), 185–196.

    Article  MathSciNet  MATH  Google Scholar 

  33. S. RICKMAN: The analogue of Picard’s theorem for quasiregular mappings in dimension three, Acta Math. 154 (1985), 195–242.

    Article  MathSciNet  MATH  Google Scholar 

  34. S. RICKMAN: Sets with large local index of quasiregular mappings in dimension three, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 493–498.

    Article  MathSciNet  MATH  Google Scholar 

  35. S. RICKMAN: Quasiregular Mappings, (to appear).

    Google Scholar 

  36. S. RICKMAN: Nonremovable Cantor sets for bounded quasiregular mappings, Preprint 42, Institut Mittag-Leffler, 1989/90.

    Google Scholar 

  37. S. RICKMAN and U. SREBRO: Remarks on the local index of quasiregular mappings, J. Analyse Math. 46 (1986), 246–250.

    Article  MathSciNet  MATH  Google Scholar 

  38. J. SARVAS: Coefficients of injectivity for quasiregular mappings, Duke Math. J. 43 (1976), 147–158.

    Article  MathSciNet  MATH  Google Scholar 

  39. S. STOÏLOW: Leçons sur les Principles Topologique de la Theorie des Functions Analytiques, Gauthier-Villars, 1938.

    Google Scholar 

  40. J. VÄISÄLÄ: Discrete open mappings on manifolds, Ann. Acad. Sci. Fenn. Ser. A I 392 (1966), 1–10.

    MathSciNet  MATH  Google Scholar 

  41. J. VÄISÄLÄ: Lectures on n-Dimensional Quasiconformal Mappings, Lecture Notes in Math. Vol. 229, Springer-Verlag, Berlin-Heidelberg-New York, 1971.

    MATH  Google Scholar 

  42. J. VÄISÄLÄ: A survey of quasiregular maps in R n, Proc. Internat. Congr. Math. (Helsniki, 1978), Vol. 2, 685–691, Acad. Sci. Fennica, Helsinki, 1980.

    Google Scholar 

  43. M. VUORINEN: Lindelöf-type theorems for quasiconformal and quasiregular mappings, Proc. Complex Analysis Semester, Banach Center Public., Vol. 11, 353–362, Warsaw, 1983.

    MathSciNet  MATH  Google Scholar 

  44. M. VUORINEN: Conformal Geometry and Quasiregular Mappings, Lecture Notes in Math. Vol. 1319, Springer-Verlag, Berlin-Heidelberg-New York, 1988.

    MATH  Google Scholar 

  45. M. VUORINEN: On Picard’s theorem for entire quasiregular mappings, Proc. Amer. Math. Soc. 15 (1989), 383–394.

    MathSciNet  MATH  Google Scholar 

  46. V. A. ZORICH: The theorem of M. A. Lavrent’ev on quasiconformal mappings in space (Russian), Mat. Sb. 74 (1967), 417–433.

    MathSciNet  Google Scholar 

  47. V. A. ZORICH: Isolated singularities of mappings with bounded distortion (Russian), Mat. Sb. 81 (1970), 634–638.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technion, Haifa, Israel

    Uri Srebro

Authors
  1. Uri Srebro
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Matti Vuorinen

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag

About this paper

Cite this paper

Srebro, U. (1992). Topological properties of quasiregular mappings. In: Vuorinen, M. (eds) Quasiconformal Space Mappings. Lecture Notes in Mathematics, vol 1508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094241

Download citation

  • DOI: https://doi.org/10.1007/BFb0094241

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55418-9

  • Online ISBN: 978-3-540-47061-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation