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

Isobe, Takeshi

doi:10.1090/S0002-9939-97-03804-5

Non-existence and uniqueness results for boundary value problems for Yang-Mills connections
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by Takeshi Isobe PDF

Proc. Amer. Math. Soc. 125 (1997), 1737-1744 Request permission

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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