Global Existence for the Seiberg-Witten Flow

preprint2010arXivOpen access

Abstract

We introduce the gradient flow of the Seiberg-Witten functional on a compact, orientable Riemannian 4-manifold and show the global existence of a unique smooth solution to the flow. The flow converges uniquely in C∞C^\infty up to gauge to a critical point of the Seiberg-Witten functional.

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