Annals of Global Analysis and Geometry

, Volume 15, Issue 1, pp 1–25 | Cite as

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

  • Andreas Schlatter


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.

geometric evolution equations vectorbundles 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adams, R.: Sobolev Spaces, Academic Press, London, 1978.Google Scholar
  2. 2.
    Atiyah, M., Hitchin, N. and Singer, I.: Self-duality in four dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A (1978), 425–461.Google Scholar
  3. 3.
    Lawson, B.: The Theory of Gauge Fields in Four Dimensions, CBMS Regional Conf. Series 58, Amer. Math. Soc., Providence, 1987.Google Scholar
  4. 4.
    Bourguignon, J. P. and Lawson, B.: Stability and isolation phenomena for Yang-Mills fields, Comm. Math. Phys. 79 (1981), 189–230.zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Donaldson, S. K. and Kronheimer, P.: The Topology of Four-Manifolds, Clarendon Press, Oxford, New York, 1990.Google Scholar
  6. 6.
    Freed, D. and Uhlenbeck, K.: Instantons and Four-Manifolds, 2nd edition, Springer-Verlag, New York, Berlin, 1991.Google Scholar
  7. 7.
    Jost, J.: Nonlinear Methods in Riemannian and Kählerian Geometry, DMV Seminar 10, Birkhäuser, Basel, 1991.Google Scholar
  8. 8.
    Lawson, B. and Michelson, M.-L.: Spin Geometry, Princeton University Press, Princeton, NJ, 1989.Google Scholar
  9. 9.
    Palais, R.: Foundations of Global Analysis, Springer-Verlag, Berlin, 1969.Google Scholar
  10. 10.
    Sedlacek, S.: The Yang-Mills functional over four-manifolds, Comm. Math. Phys. 86 (1982), 515–527.zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Struwe, M.: The evolution of harmonic maps of Riemannian surfaces, Commentarii Mathematici Helvetici 60 (1985), 558–581.zbMATHMathSciNetGoogle Scholar
  12. 12.
    Struwe, M.: The Yang-Mills flow in four dimensions, Calc. Var. 2 (1994) 123–150.zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Uhlenbeck, K.: Connections with Lp — bounds on curvature, Comm. Math. Phys. 83 (1982) 31–42.zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Uhlenbeck, K.: Removable singularities in Yang-Mills fields, Comm. Math. Phys. 83 (1982), 11–30.zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Uhlenbeck, K.: The Chern classes of Sobolev connections, Comm. Math. Phys. 101 (1985), 449–457.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Andreas Schlatter
    • 1
  1. 1.KüttigenSwitzerland

Personalised recommendations