Skip to main content
SpringerLink
Log in

Equivariant harmonic maps into the sphere via isoparametric maps

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

By using concrete isoparametric maps we obtain some new equivariant harmonic maps between spheres and solve equivariant boundary value problems for harmonic maps from unit open ballB m+1 intoS n.

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

Similar content being viewed by others

References

  1. Carter, S and West, A.: Isoparametric systems and transnormality. Proc. London Math. Soc. (3)51,520–542(1985)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ding, W. Y.: Symmetric harmonic maps betwen spheres. Comm. Math. Phys.118,41–649(1988)

    Article  Google Scholar 

  3. Eells, J and Lemaire, L.: A report on harmonic maps. Bull. London Math. Soc.10,1–68(1978)

    Article  MathSciNet  MATH  Google Scholar 

  4. Eells, J. and Lemaire, L.: Examples of harmonic maps from disks to hemispheres. Math. Z.185,517–519(1984)

    Article  MathSciNet  MATH  Google Scholar 

  5. Eells, J.: On equivariant harmonic maps. Proc. 1981, Shanghai Symposium on Differential Geometry and Differential Equations Science Press, 55–73(1984)

  6. Eells, J. and Lemaire, L.: Another report on harmonic maps. Bull. London Math. Soc.20,385–524(1988)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ferus, D. and Karcher, H.: Non-rotational minimal spheres and minimal cones. Comment. Math. Helv.60,247–269(1985)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hamilton, R. T.:Harmonic Maps of Manifolds with Boundary. Lecture Notes Math.,471 Springer-Verlag (1975)

  9. Hardt, R.: Axially symmetric harmonic maps. Proc. Workshop on ‘Defects Singularities and Patterns in Nematic Liquid Crystals: Mathematics and Physics Aspects', Université Paris-Sud (1990).

  10. Hart, R., Kinderlehrer, D. and Lin, F.H.: Existence and partial regularity of static liquid configurations. Comm. Math. Phys.105, 547–570(1986)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hardt, R., Kinderlehrer, D. and Lin, F. H.: The variety of configuration of static liquid crystals. Progress in Nonlinear diff. Eqs. and Their Applications, Vol.4, Birkhäuser, 115–132(1990)

    MathSciNet  MATH  Google Scholar 

  12. Hardt, R., Lin, F. H. and Poon, C. C.: Axially symmetric harmonic maps minimizing a relaxed energy. Comm. Pure and Appl. Math., V.XLV,417–459(1992)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hildebrandt, S.: Nonlinear elliptic systems and harmonic mappings. Proc. Beijing Symposium on Differential Geometry and Differential Equations, 1980, Gordon and Breach, 481–615 (1983)

  14. Hildebrandt, S, Kaul, H. and Widman, K. O.: An existence theorem for harmonic mappings of Riemanian manifolds, Acta Math.138,1–16(1977)

    Article  MathSciNet  MATH  Google Scholar 

  15. Jäger, M. and Kaul, H.: Rotationally symmetric harmonic maps from ball into a sphere and the regularity problem for weak solutions of elliptic systems. J. Reine Angew. Math.343,146–161(1983)

    MathSciNet  MATH  Google Scholar 

  16. Morrey, Jr. C. B.:Multiple integrals in the calculus of variations. Springer-Verlag (1966).

  17. Pettinati, V. and Ratto, A.: Existence and non-existence results for harmonic maps between spheres. Ann. SNS Piaa Ser. IV,17,273–282(1990)

    MATH  Google Scholar 

  18. Smith, R. T.: Harmonic mappings of spheres. Amer. J. Math.97, 367–385(1975)

    Article  MathSciNet  Google Scholar 

  19. Teng, C. L.: Isoparametric submanifolds and their coxter groups. J. Diff. Geom.21,79–107(1985)

    Article  Google Scholar 

  20. Wang, Qiming: Isoparametric maps of Riemannian manifolds and their applications. Adv. Science China. Math. V. 2,79–103(1988)

    Google Scholar 

  21. Xin, Y. L.: Riemannian submersions and equivariant harmonic maps. Proc. Diff. Geom. in Honour of Professor Su Bachin, World Scientific Publ. co. (to appear)

  22. Zhang, D.: The existence of nonminimal regular harmonic maps formB 3 toS 2, Ann. SNS Pisa Ser.IV16,355–365(1989)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Fudan University, Shanghai, China

    Y. L. Xin

  2. International Center for Theoretical Physics, Trieste, Italy

    Y. L. Xin

Authors
  1. Y. L. Xin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research partially supported by NNSFC, SFECC and ICTP.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xin, Y.L. Equivariant harmonic maps into the sphere via isoparametric maps. Manuscripta Math 79, 49–71 (1993). https://doi.org/10.1007/BF02568328

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568328

Keywords

Search

Navigation