Communications in Analysis and Geometry

Volume 18 (2010)

Number 3

Global existence for the Seiberg–Witten flow

Pages: 433 – 473

DOI: https://dx.doi.org/10.4310/CAG.2010.v18.n3.a2

Authors

Min-Chun Hong (Department of Mathematics, The University of Queensland, Australia)

Lorenz Schabrun (Department of Mathematics, The University of Queensland, Australia)

Abstract

We introduce the gradient flow ofthe Seiberg–Witten functional on a compact, orientable Riemannian4-manifold and show the global existence of a unique smoothsolution to the flow. The flow converges uniquely in $C^\infty$up to gauge to a critical point of the Seiberg–Witten functional.

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Published 1 January 2010