Skip to main content

Examples of harmonic and holomorphic maps

  • 327 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 798)

Keywords

  • Riemann Surface
  • Minimal Surface
  • Meromorphic Function
  • Fundamental Form
  • Compact Surface

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. DELAUNAY, C.: Sur la surface de révolution dont la courbure moyenne est constante. J.Math. pures et appl. Sér. 1(6) (1841), 309–320; with a note appended by M.STURM.

    Google Scholar 

  2. EELLS,J.: Harmonic maps of surfaces, Proc. Eighth Annual National Mathematics Conference, Tehran. Bull. Iranian Math. Soc. (1978).

    Google Scholar 

  3. —: On the surfaces of Delaunay and their Gauss maps, Fourth Coloq. Inter. Geo. Dif. (In honour of Professor E.Vidal), Santiago de Compostela.

    Google Scholar 

  4. — and L. LEMAIRE: A report on harmonic maps, Bull. London Math. Soc. 10 (1978), 1–68.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. — and —: On the construction of harmonic and holomorphic maps between surfaces, to appear.

    Google Scholar 

  6. — and J.H. SAMPSON: Harmonic mapping of Riemannian manifolds, Ann. J. Math. 86 (1964), 109–160.

    MathSciNet  MATH  Google Scholar 

  7. — and J.C. WOOD: Restrictions on harmonic maps of surfaces, Topology 15 (1976), 263–266.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. KENMOTSU, K.: Weierstrass formula for surfaces of prescribed mean curvature, to appear.

    Google Scholar 

  9. MEEKS, W.H.: The conformal structure and geometry of triply periodic minimal surfaces in ℝ3, Bull. Am. Math. Soc. 83 (1977), 134–6.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. NAGANO, T. and B. SMYTH: Sur les surfaces minimales hyperelliptique dans un tore, C.R. Paris A280 (1975), 1527–1529.

    MathSciNet  MATH  Google Scholar 

  11. — and —: Periodic minimal sufaces, Comm. Math. Helv. (1978).

    Google Scholar 

  12. RUH, E.A. and J. VILMS:, The tension field of the Gauss map. Trans. Am. Math. Soc. 149 (1970), 509–513.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. SMITH, R.T.: Harmonic mapping of spheres, Warwick Thesis (1972).

    Google Scholar 

  14. THOMPSON, D'A.W.: Growth and Form, Cambridge (1917).

    Google Scholar 

  15. VILMS, J.: Submanifolds of Euclidean space with parallel second fundamental form, Proc. Ann. Math. Soc. 32 (1972), 263–267.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Eells, J. (1980). Examples of harmonic and holomorphic maps. In: Ławrynowicz, J. (eds) Analytic Functions Kozubnik 1979. Lecture Notes in Mathematics, vol 798. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097261

Download citation

  • DOI: https://doi.org/10.1007/BFb0097261

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09985-7

  • Online ISBN: 978-3-540-39247-7

  • eBook Packages: Springer Book Archive