Skip to main content
SpringerLink
Log in

Harmonic hereditary convexity

  • Research
  • Published:
Complex Analysis and its Synergies Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Chuaqui, M., Duren, P., Osgood, B.: Ellipses, near ellipses, and harmonic Möbius transformations. Proc. Amer. Math. Soc. 133, 2705–2710 (2005)

    Article  MathSciNet  Google Scholar 

  2. Clunie, J., Sheil-Small, T.: Harmonic univalent functions. Ann. Acad. Sci. Fenn. Math. 9, 3–25 (1984)

    Article  MathSciNet  Google Scholar 

  3. Duren, P.: Univalent functions. Springer-Verlag, New York (1983)

    MATH  Google Scholar 

  4. Duren, P.: Harmonic Mappings in the Plane. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  5. Hengartner, W., Schober, G.: Harmonic mappings with given dilatation. J. London Math. Soc. 33, 473–483 (1986)

    Article  MathSciNet  Google Scholar 

  6. Iwaniec, T., Koh, N., Kovalev, L.V., Onninen, J.: Existence of energy-minimal diffeomorphisms between doubly connected domains. Invent. Math. 186, 667–707 (2011)

    Article  MathSciNet  Google Scholar 

  7. Iwaniec, T., Kovalev, L.V., Onninen, J.: The harmonic mapping problem and affine capacity. Proc. Roy. Soc. Edinburgh Sect. A 141, 1017–1030 (2011)

    Article  MathSciNet  Google Scholar 

  8. Kalaj, D.: Energy-minimal diffeomorphisms between doubly connected Riemann surfaces. Calc. Var. Partial Differential Equations 51, 465–494 (2014)

    Article  MathSciNet  Google Scholar 

  9. Koh, N.: Hereditary convexity for harmonic homeomorphisms. Indiana University Mathematics Journal 64, 231–243 (2015)

    Article  MathSciNet  Google Scholar 

  10. Koh, N.: Hereditary circularity for energy minimal diffeomorphisms. Conform. Geom. Dyn. 21, 369–377 (2017)

    Article  MathSciNet  Google Scholar 

  11. Koh, N.: Harmonic mappings with hereditary starlikeness. J. Math. Anal. Appl. 457(1), 273–286 (2018)

    Article  MathSciNet  Google Scholar 

  12. Koh, N., Kovalev, L.V.: Area contraction for harmonic automorphisms of the disk. Bull. London Math. Soc. 43, 91–96 (2011)

    Article  MathSciNet  Google Scholar 

  13. Lehto, O., Virtanen, K.: Quasiconformal Mappings in the Plane. Springer-Verlag, Berlin (1973)

    Book  Google Scholar 

  14. Lewy, H.: On the non-vanishing of the Jacobian in certain one-to-one mappings. Bull. Amer. Math. Soc. 42, 689–692 (1936)

    Article  MathSciNet  Google Scholar 

  15. Nagpal, S., Ravichandran, V.: Fully starlike and fully convex harmonic mappings of order \(\alpha\). Ann. Polon. Math. 108, 85–107 (2013)

    Article  MathSciNet  Google Scholar 

  16. Radó, T.: Zu einem Satze von S. Bernstein über Minimalflächen im Großen. Math. Z. 26, 559–565 (1927)

    Article  MathSciNet  Google Scholar 

  17. Ruscheweyh, S., Salinas, L.C.: On the preservation of direction-convexity and the Goodman-Saff conjecture. Ann. Acad. Sci. Fenn. Math. 14, 63–73 (1989)

    Article  MathSciNet  Google Scholar 

  18. Schiff, J.L.: Normal families. Springer-Verlag, New York (1993)

    Book  Google Scholar 

  19. Study, E.: Vorlesungen über ausgewählte Gegenstände der Geometrie. Heft II, Teubner, Leipzig (1913)

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand

    Ngin-Tee Koh

Authors
  1. Ngin-Tee Koh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ngin-Tee Koh.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Koh, NT. Harmonic hereditary convexity. Complex Anal Synerg 7, 9 (2021). https://doi.org/10.1007/s40627-021-00074-z

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s40627-021-00074-z

Search

Navigation