Some Energy Properties of Yang-Mills Connections

2015/02/11 by Teng Huang, Huang, Teng
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1502.03198

openalex publication_date 2015/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a vector bundle E over a compact Riemannian manifold M=Mⁿ,n≥ 4,and A is a Yang-Mills connection with L^(n)/(2) curvature F_A on E.Then we prove a mean value inequality for the density |F_A|^(n)/(2).This inequality give rise to an energy concentrate principle for sequences of solutions that have bounded energy.We also proof that the energy must be bounded from below by some positive constant unless E is a flat bundle.

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