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


Author: Takeshi Isobe
Journal: Proc. Amer. Math. Soc. 125 (1997), 1737-1744
MSC (1991): Primary 35J50, 58E15, 81T13
DOI: https://doi.org/10.1090/S0002-9939-97-03804-5
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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Additional Information

Takeshi Isobe
Affiliation: Department of Mathematics, Faculty of Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan
Email: isobe@math.titech.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-97-03804-5
Keywords: Yang-Mills, boundary value problems, non-existence, uniqueness
Received by editor(s): December 8, 1995
Communicated by: Ronald Stern
Article copyright: © Copyright 1997 American Mathematical Society

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