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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© 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
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