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arXiv · 1608.05463

Heat flow of Yang-Mills-Higgs functionals in dimension two

Chong Song·Changyou Wang
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Abstract

We consider the heat flow of Yang-Mills-Higgs functional where the base manifold is a Riemannian surface and the fiber is a compact symplectic manifold. We show that the corresponding Cauchy problem admits a global weak solution for any $H^1$-initial data. Moreover, the solution is smooth except finitely many singularities. We prove an energy identity at finite time singularities and give a description of the asymptotic behavior at time infinity.

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Chong Song, Changyou Wang. 2016-08-19. Heat flow of Yang-Mills-Higgs functionals in dimension two. https://arxiv.org/abs/1608.05463

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