1. CJM 2005 (vol 57 pp. 871)
 Zhang, Xi

Hermitian Yang_MillsHiggs Metrics on\\Complete KÃ¤hler Manifolds
In this paper, first, we will investigate the
Dirichlet problem for one type of vortex equation, which
generalizes the wellknown Hermitian Einstein equation. Secondly,
we will give existence results for solutions of these vortex
equations over various complete noncompact K\"ahler manifolds.
Keywords:vortex equation, Hermitian YangMillsHiggs metric,, holomorphic vector bundle, KÃ¤hler manifolds Categories:58E15, 53C07 

2. CJM 2000 (vol 52 pp. 695)
 Carey, A.; Farber, M.; Mathai, V.

Correspondences, von Neumann Algebras and Holomorphic $L^2$ Torsion
Given a holomorphic Hilbertian bundle on a compact complex manifold, we
introduce the notion of holomorphic $L^2$ torsion, which lies in the
determinant line of the twisted $L^2$ Dolbeault cohomology and
represents a volume element there. Here we utilise the theory of
determinant lines of Hilbertian modules over finite von~Neumann
algebras as developed in \cite{CFM}. This specialises to the
RaySingerQuillen holomorphic torsion in the finite dimensional case.
We compute a metric variation formula for the holomorphic $L^2$
torsion, which shows that it is {\it not\/} in general independent of
the choice of Hermitian metrics on the complex manifold and on the
holomorphic Hilbertian bundle, which are needed to define it. We
therefore initiate the theory of correspondences of determinant lines,
that enables us to define a relative holomorphic $L^2$ torsion for a
pair of flat Hilbertian bundles, which we prove is independent of the
choice of Hermitian metrics on the complex manifold and on the flat
Hilbertian bundles.
Keywords:holomorphic $L^2$ torsion, correspondences, local index theorem, almost KÃ¤hler manifolds, von~Neumann algebras, determinant lines Categories:58J52, 58J35, 58J20 
