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Energy gaps for $$p$$-Yang-Mills fields over compact Riemannian manifolds. (English) Zbl 1408.58011
The main purpose of the present paper is to obtain a Simons-type inequality for $$p$$-Yang-Mills fields over an oriented compact manifold without boundary. Next, the author establishes some $$L^r$$-energy gaps of $$p$$-Yang-Mills fields. The problem of energy gaps for $$p$$-Yang-Mills fields over complete noncompact Riemannian manifolds remains open.
##### MSC:
 5.8e+16 Variational problems concerning extremal problems in several variables; Yang-Mills functionals 5.8e+21 Harmonic maps, etc.
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