Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Non-existence and uniqueness results for boundary value problems for Yang-Mills connections

Author(s): Takeshi Isobe
Journal: Proc. Amer. Math. Soc. 125 (1997), 1737-1744.
MSC (1991): Primary 35J50, 58E15, 81T13
MathSciNet review: 1376764
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Abstract: We show uniqueness results for the Dirichlet problem for Yang-Mills connections defined in $n$ -dimensional ( $n\ge 4$ ) star-shaped domains with flat boundary values. This result also shows the non-existence result for the Dirichlet problem in dimension 4, since in 4-dimension, there exist countably many connected components of connections with prescribed Dirichlet boundary value. We also show non-existence results for the Neumann problem. Examples of non-minimal Yang-Mills connections for the Dirichlet and the Neumann problems are also given.

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