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Ck-bound of curvatures in Yang-Mills theory

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1255)

Abstract

We generalize here the theorem in [1] to the case of Yang-Mills theory. The smoothing of the connection is achieved by using the evolution equation of Yang-Mills action. We obtain the Ck-bound of curvatures of new connection in terms of the Co-bound of curvatures of the original connection. As an application, we prove that the evolution ecuation has a unique solution for a maximal time interval 0≤t<T*≤∞. If T*<∞, then Sup ||F|| →∞ as t→T*.

Keywords

  • Curvature Form
  • Maximal Time Interval
  • Riemannian Curvature
  • Injectivity Radius
  • Riemannian Curvature Tensor

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References

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© 1987 Springer-Verlag

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Shen, Cl. (1987). Ck-bound of curvatures in Yang-Mills theory. In: Gu, C., Berger, M., Bryant, R.L. (eds) Differential Geometry and Differential Equations. Lecture Notes in Mathematics, vol 1255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077684

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  • DOI: https://doi.org/10.1007/BFb0077684

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17849-1

  • Online ISBN: 978-3-540-47883-6

  • eBook Packages: Springer Book Archive