Gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincar\'e inequality

24 Jan 2019  ·  Vieira Matheus ·

This paper provides two gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincar\'e inequality. The results show that given a Yang-Mills connection on a vector bundle over the manifold if the positive part of the curvature satisfies a certain upper bound then it is identically zero... The theorems can be applied to many examples of manifolds including the model spaces of constant sectional curvature and constant holomorphic sectional curvature. read more

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Differential Geometry Mathematical Physics Mathematical Physics