Canad. J. Math. 57(2005), 871-896
Printed: Aug 2005
In this paper, first, we will investigate the
Dirichlet problem for one type of vortex equation, which
generalizes the well-known Hermitian Einstein equation. Secondly,
we will give existence results for solutions of these vortex
equations over various complete noncompact K\"ahler manifolds.
vortex equation, Hermitian Yang--Mills--Higgs metric, holomorphic vector bundle, Kähler manifolds
58E15 - Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.
53C07 - Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20]