Abstract
Global existence and uniqueness is established for the Yang-Mills heat flow in a vector bundle over a compact Riemannian four-manifold for given initial connection of finite energy. Our results are analogous to those valid for the evolution of harmonic maps of Riemannian surfaces.
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The author gratefully acknowledges the hospitality and support of Princeton University, the Institute for Advanced Study, and the École Normale Supérieure Cachan.
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