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Title:
The Yang-Mills-Higgs Flow in the Neighbourhood of a Critical Point
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Abstract:
The Yang-Mills-Higgs flow was originally studied by Simpson in the context of constructing Hermitian-Einstein metrics on Higgs bundles. Methods of Donaldson and Simpson show that the Yang-Mills-Higgs flow resembles a nonlinear heat equation on the space of Hermitian metrics on the bundle and therefore the downwards flow is well-behaved with respect to existence and uniqueness, and it also has nice smoothing properties. On the other hand, the upwards flow is ill-posed and therefore even existence of solutions is problematic.
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