Communications in Mathematical Physics

, Volume 83, Issue 1, pp 31–42 | Cite as

Connections withL P bounds on curvature

  • Karen K. Uhlenbeck


We show by means of the implicit function theorem that Coulomb gauges exist for fields over a ball inR n when the integralLn/2 field norm is sufficiently small. We then are able to prove a weak compactness theorem for fields on compact manifolds withL p integral norms bounded,p>n/2.


Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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  1. 1.
    Bourguignon, J. P. Lawson, H. B., Jr.: Commun. Math. Phys.79, 189–230 (1981)Google Scholar
  2. 2.
    Hamilton, R.: Harmonic maps of manifolds with boundary. In: Lecture Notes in Mathematics, Vol. 471 Berlin, Heidelberg, New York: Springer 1975Google Scholar
  3. 3.
    Husemoller, D.: Fibre bundles (Chap. 5). In: Graduate Texts in Mathematics, Vol. 20. Berlin, Heidelberg, New York: Springer 1966Google Scholar
  4. 4.
    Morrey, C. B., Jr.: Multiple integrals in the calculus of variations. Berlin, Heidelberg, New York: Springer 1966Google Scholar
  5. 5.
    Palais, R. S.: Foundations of global non-linear analysis. New York: Benjamin, 1968Google Scholar
  6. 6.
    Steenrod, N.: The topology of fibre bundles (Part I). Princeton, New Jersey: Princeton University Press, 1951Google Scholar
  7. 7.
    Taubes, C.: Existence of multimonopole solutions to the static SU (2) Yang-Mills-Higgs equations in the Prasad-Summerfield limit. See Jaffe, A. and Taubes, C., Vortices and Monopoles, Boston: Birkhäuser 1980Google Scholar
  8. 8.
    Uhlenbeck, K.: Removable singularities in Yang-Mills fields, Commun. Math. Phys.83, 11–29 (1982)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Karen K. Uhlenbeck
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Chicago CircleChicagoUSA

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