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| In this paper, we will investigate one type of vortex equations over various complete noncompact Hermitian manifolds, the related metric will be called Hermitian Yang-Mills-Higgs metric. Using the solvability of Dirichlet problem in [16] and compact exhaustion method, we can solve these Vortex equation on complete Hermitian manifold, under some conditions on the complete Hermitian manifold and the initial Hermitian metric. Then, we obtain a existence theorem of Hermitian Yang-Mills-Higgs metric on complete Hermitian manifold, this result can be seen as a generalization of the result about Hermitian Yang-Mills metrics in [22]. |
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| Keywords:Vortex equation;holomorphic vector bundle;Hermitian manifold |
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