The gauge fixing theorem with applications to the Yang-Mills flow over Riemannian manifolds

2017/01/03 by Hong, Min-Chun
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.00601

Abstract

In 1982, Uhlenbeck \cite U2 established the well-known gauge fixing theorem, which has played a fundamental role for Yang-Mills theory. In this paper, we apply the idea of Uhlenbeck to establish a parabolic type of gauge fixing theorems for the Yang-Mills flow and prove existence of a weak solution of the Yang-Mills flow on a compact n-dimensional manifold with initial value A₀ in W^1,n/2(M). When n=4, we improve a key lemma of Uhlenbeck (Lemma 2.7 of \cite U2) to prove uniqueness of weak solutions of the Yang-Mills flow on a four dimensional manifold.

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