Heat flow for the Yang-Mills-Higgs field and the Hermitian-Yang-Mills-Higgs metric

Research Report MRR99-009

Heat flow for the Yang-Mills-Higgs field and the Hermitian-Yang-Mills-Higgs metric

Min-Chun Hong

Abstract: For a parameter $\lambda >0$ , we study a new type of vortex equations, which generalize the well-known Hermitian-Einstein equation, for a connection A and a section $\phi$ of a holomorphic vector bundle E over a Kähler manifold X. We establish global existence of smooth solutions to heat flow for a self-dual Yang-Mills-Higgs field on E. Assuming the $\lambda$ -stability of $(E, \phi )$ , we prove the existence of the Hermitian Yang-Mills-Higgs metric on the holomorphic bundle E by studying the limiting behaviour of the gauge flow.

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