Title: Einstein Type Metrics and Stability on Vector Bundles.

Abstract:

	In this paper we show that stability for holomorphic
vector bundles are equivalent to existence of solutions to certain
system fo Monge Ampere equations parametrized by a parameter $k$.
We solve these fully nonlinear elliptic system by singular perturbation
technique and show that the vanishing of obstructions
for the perturbation is given precisely by the stability condition.
This can be interpreted as an infinite dimensional analog of the
equivalency between Geometric Invariant Theory and Symplectic Reduction
for moduli space of vector bundles.