Long-time existence for Yang–Mills flow

  • Alex WaldronEmail author


We establish that finite-time singularities do not occur in four-dimensional Yang–Mills flow, confirming the conjecture of Schlatter et al. (Am J Math 120:117–128, 1998). The proof relies on a weighted energy identity and sharp decay estimates in the neck region.



The author thanks Simon Donaldson, Song Sun, Xiuxiong Chen, and Yuanqi Wang for their encouragement and for participating in a preprint seminar, as well as the anonymous referee for valuable comments. He also thanks Michael Struwe and Toti Daskalopoulos for discussions during the Oberwolfach workshop “Nonlinear Evolution Problems” in June 2016.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Simons Center for Geometry and PhysicsStony BrookUSA

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