Skip to main content
Log in

Long-Time Behaviour of the Yang--Mills Flow in Four Dimensions

  • Published:
Annals of Global Analysis and Geometry Aims and scope Submit manuscript

Abstract

We investigate the long-time behaviour and the behaviour at singularities of the Yang--Mills heat flow in four dimensions with finite energy initial data. In addition we shall give an upper bound for the total number of singularities.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Adams, R.: Sobolev Spaces, Academic Press, London, 1978.

    Google Scholar 

  2. Atiyah, M., Hitchin, N. and Singer, I.: Self-duality in four dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A (1978), 425–461.

  3. Lawson, B.: The Theory of Gauge Fields in Four Dimensions, CBMS Regional Conf. Series 58, Amer. Math. Soc., Providence, 1987.

    Google Scholar 

  4. Bourguignon, J. P. and Lawson, B.: Stability and isolation phenomena for Yang-Mills fields, Comm. Math. Phys. 79 (1981), 189–230.

    Article  MATH  MathSciNet  Google Scholar 

  5. Donaldson, S. K. and Kronheimer, P.: The Topology of Four-Manifolds, Clarendon Press, Oxford, New York, 1990.

    Google Scholar 

  6. Freed, D. and Uhlenbeck, K.: Instantons and Four-Manifolds, 2nd edition, Springer-Verlag, New York, Berlin, 1991.

    Google Scholar 

  7. Jost, J.: Nonlinear Methods in Riemannian and Kählerian Geometry, DMV Seminar 10, Birkhäuser, Basel, 1991.

    Google Scholar 

  8. Lawson, B. and Michelson, M.-L.: Spin Geometry, Princeton University Press, Princeton, NJ, 1989.

    Google Scholar 

  9. Palais, R.: Foundations of Global Analysis, Springer-Verlag, Berlin, 1969.

    Google Scholar 

  10. Sedlacek, S.: The Yang-Mills functional over four-manifolds, Comm. Math. Phys. 86 (1982), 515–527.

    Article  MATH  MathSciNet  Google Scholar 

  11. Struwe, M.: The evolution of harmonic maps of Riemannian surfaces, Commentarii Mathematici Helvetici 60 (1985), 558–581.

    MATH  MathSciNet  Google Scholar 

  12. Struwe, M.: The Yang-Mills flow in four dimensions, Calc. Var. 2 (1994) 123–150.

    Article  MATH  MathSciNet  Google Scholar 

  13. Uhlenbeck, K.: Connections with Lp — bounds on curvature, Comm. Math. Phys. 83 (1982) 31–42.

    Article  MATH  MathSciNet  Google Scholar 

  14. Uhlenbeck, K.: Removable singularities in Yang-Mills fields, Comm. Math. Phys. 83 (1982), 11–30.

    Article  MATH  MathSciNet  Google Scholar 

  15. Uhlenbeck, K.: The Chern classes of Sobolev connections, Comm. Math. Phys. 101 (1985), 449–457.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schlatter, A. Long-Time Behaviour of the Yang--Mills Flow in Four Dimensions. Annals of Global Analysis and Geometry 15, 1–25 (1997). https://doi.org/10.1023/A:1006541305639

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006541305639

Navigation